The volume of the rectangular prism with the same dimensions as the rectangular pyramid is 300 cubic centimeters.
What is rectangular prism?A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional solid shape with six rectangular faces, where each pair of opposite faces are congruent (i.e., have the same dimensions) and parallel to each other.
The rectangular prism is defined by three dimensions: length, width, and height. The length is the longest dimension of the prism, the width is the second-longest dimension, and the height is the shortest dimension, perpendicular to both length and width. The volume of a rectangular prism is given by the formula: V = l * w * h.
In the given question,
Let's assume that the rectangular pyramid has a rectangular base with length l, width w, and height h. The formula for the volume of a rectangular pyramid is given by:
V_pyramid = (1/3) * base_area * height
where base_area = l * w is the area of the rectangular base of the pyramid.
We know that the volume of the rectangular pyramid is 100 cm^3, so we can write: 100 = (1/3) * l * w * h
Simplifying this equation, we get:
l * w * h = 300
Now, let's find the volume of the rectangular prism with the same dimensions. The formula for the volume of a rectangular prism is given by: V_prism = base_area * height
where base_area = l * w is the area of the rectangular base of the prism.
Since the rectangular prism has the same dimensions as the rectangular base of the pyramid, its volume is given by: V_prism = l * w * h
Substituting the value of l * w * h from the equation we derived earlier, we get: V_prism = 300
Therefore, the volume of the rectangular prism with the same dimensions as the rectangular pyramid is 300 cubic centimeters.
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if cell phone companies screen text messages, then freedom of speech is threatened. thus, freedom of speech is not threatened, because cell phone companies do not screen text messages. which of the following correctly expresses the form of this argument? a. if c then f. b. not f. c. all c are f. d. if c then f. e. if c then f. not
The correct option that expresses the form of the given argument is "d. if c then f."Explanation:In the given argument, it is stated that if cell phone companies screen text messages, then freedom of speech is threatened.
But as cell phone companies do not screen text messages, so freedom of speech is not threatened. This is a conditional argument, and it can be expressed in the form of a hypothetical syllogism.
The hypothetical syllogism is a syllogism that has a conditional statement in its premises. It is also called a chain argument or transitive argument. The form of the hypothetical syllogism is "If A, then B. If B, then C.
Therefore, if A, then C."In the given argument, it can be expressed in the form of the hypothetical syllogism as follows:If cell phone companies screen text messages, then freedom of speech is threatened. If freedom of speech is threatened, then cell phone companies screen text messages. Therefore, if cell phone companies do not screen text messages, then freedom of speech is not threatened.This can also be represented as "if C then F."Therefore, the correct option that expresses the form of the given argument is "d. if c then f."
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A simplified carbon cycle with aerobic and anaerobic processes is depicted here. Although much of the emphasis on global climate change has been on increasing carbon dioxide levels, methane is also a greenhouse gas whose levels are increasing due to human and other activity. Which of these actions would increase methane levels in the atmosphere and potentially affect global climate change? Select ALL that apply.
--------------------------------------------------------------------------------------------------------------------------------
A Agricultural practices in rice cultivation releases methane.Agricultural practices in rice cultivation releases methane.
B Anaerobic digestion of cellulose by cows produces methane.Anaerobic digestion of cellulose by cows produces methane.
C Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.
D Industrial combustion of fossil fuels releases methane into the atmosphere.Industrial combustion of fossil fuels releases methane into the atmosphere.
E Anaerobic decomposition of landfill material releases methane into the atmosphere.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
what is equation ?A mathematical equation is a claim that two expressions are equal, typically represented with an equal sign (=) between them. The terms "left hand side" (LHS) and "right hand side" (RHS) of the equation, respectively, refer to the expressions on either side of the equal sign. Equations are a common tool for problem solving because they may be used to depict relationships between variables or quantities and to determine the value(s) of the unknown variable(s) that satisfies the equation. For instance, the link between the variables x and the integers 2, 5, and 11 is represented by the equation 2x + 5 = 11. Finding the value of x that makes the left and right sides of the equation equal is necessary to solve this equation.
given
A) Rice farming operations release methane into the atmosphere.
B) Methane is created when cows break down cellulose anaerobically.
E) Methane is released into the atmosphere when landfill material decomposes anaerobically.
Any of the aforementioned behaviours would raise the atmospheric methane concentrations and may have an impact on climate change globally.
Methane is a greenhouse gas that causes the atmosphere of the Earth to warm.
It is produced by both natural and artificial processes. Examples of human activities that contribute to methane emissions into the atmosphere include the production of rice, cattle digestion, and landfill decomposition.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
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A car travelling at a constant speed travels 60 km 30 minutes .how far will it travel in 2hrs,if it continues at the same constant speed
Answer: 240 miles in 2 hours
Step-by-step explanation:
we know the car is traveling 60 km per half hour (30 minutes)
so to find km per hour, multiply both by 2.
the rate of speed is 120 miles per 60 minutes (1 hour)
multiply 120 mph by the 2 hours given = 240 miles in 2 hours
Answer:
240 km in 2 hours
Step-by-step explanation:
If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:
Speed = distance ÷ time
Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour
Since the car is traveling at a constant speed, we can use the formula:
Distance = Speed × Time
To find how far the car will travel in 2 hours, we can substitute the values we have found:
Distance = Speed × Time
Distance = 120 km/hour × 2 hours
Distance = 240 km
Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.
auditors compared opinions about treatment (very good/acceptable/poor) at four va hospitals (labeled a,b,c,d) among veterans aged 50 and above. what are the hypotheses for a chi-square test of independence on the data? select one:
The hypotheses for a chi-square test of independence on the data that auditors compared opinions about treatment (very good/acceptable/poor) at four VA hospitals (labeled a,b,c,d) among veterans aged 50 and above are:
Null hypothesis, H0: There is no association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.
Alternative hypothesis, Ha: There is an association between the opinions about treatment of the VA hospitals and veterans aged 50 and above.
Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.
An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.
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25 out of 68 students have vanilla ice cream and the rest have chocolate. What is the ratio of the number of students who have vanilla to the total number of students?
Answer: The total number of students is the sum of the number of students who have vanilla and those who have chocolate:
Total = 25 + (68 - 25) = 43
The ratio of the number of students who have vanilla to the total number of students is:
Vanilla : Total = 25 : 43
This ratio cannot be simplified any further because 25 and 43 do not have any common factors other than 1. Therefore, the ratio of the number of students who have vanilla to the total number of students is:
25 : 43
Step-by-step explanation:
y is inversely proportional to the square of x. It is given that y = 8 for a particular value of x. k= When x increases by 300%, find the new value of y,
Answer:
1/2 or .5
Step-by-step explanation:
If y is inversely proportional to the square of x, we can express this relationship using the formula:
y = k/x^2
where k is a constant of proportionality. We are told that y = 8 for a particular value of x, so we can substitute these values into the equation:
8 = k/x^2
To find the value of k, we can solve for it:
k = 8x^2
Now we are asked to find the new value of y when x increases by 300%. This means that the new value of x will be 4 times the original value (since an increase of 300% means an increase by a factor of 3, and we need to add the original value to get the new value). So we can substitute 4x for x in our equation:
y = k/(4x)^2 = k/16x^2
We already know the value of k, so we can substitute it in and simplify:
y = (8x^2)/(16x^2) = 1/2
Therefore, the new value of y is 1/2 when x increases by 300%.
a certain congressional committee consists of 13 senators and 9 representatives. how many ways can a subcommittee of 5 be formed if at least 2 of the members must be representatives?
Answer:
Step-by-step explanation:
At the book store, you purchased some $3 clearance mystery books and $8 regular-priced science fiction books. How many of each did you buy if you spent a total of $77?
Answer:
we bought 12 $3 clearance mystery books and 5 $8 regular-priced science fiction books.
Step-by-step explanation:
how many liters of a 25 % 25%, percent saline solution must be added to 3 33 liters of a 10 % 10, percent saline solution to obtain a 15 % 15, percent saline solution?'
Answer:
Here, x represents the amount (in liters) of the 25% saline solution to be added.
We can see that the 25% saline solution needs to be mixed with the 10% saline solution to obtain a mixture that is 15% saline. The ratio of the volumes of the 25% and 10% solutions can be found by subtracting the concentrations of the two solutions and dividing by the difference between the desired concentration and the concentration of the 10% solution:
x / (3.33 - x) = (15 - 10) / (25 - 10) = 5/15 = 1/3
Multiplying both sides by 3.33 - x, we get:
x = (1/3) (3.33 - x)
Multiplying both sides by 3, we get:
3x = 3.33 - x
Solving for x, we get:
x = 0.833 liters
Therefore, 0.833 liters of the 25% saline solution must be added to 3.33 liters of the 10% saline solution to obtain 4.163 liters of a 15% saline solution.
Step-by-step explanation:
How much was one movie ticket in 2008
Answer: 7 dollars 18 cents.
Step-by-step explanation:
Jayden evaluated the expression a + (2 + 1. 5) for a = 14. He said that the value of the expression was 8. 5. Select all the statements that are true. Jayden's solution is incorrect. Jayden added inside the parentheses before dividing. Jayden substituted the wrong value for a. Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
It is true that Jayden's solution is incorrect. It is false that Jayden added inside the parentheses before dividing.
It is false that Jayden substituted the wrong value for a. It is true that Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
1) The correct solution is
Given,
a ÷ (2 + 1. 5)
Substituting the value of a which is 14
= 14 ÷ (2 + 1. 5)
= 14 ÷ 3.5
= 4
2) As there is no term which needs to be divided so, the second statement is false.
3) Jayden didn't substitute the wrong value of a he just solved the given expression without considering the bracket and divided the 14 which is the value of a by 2.
4) Jyaden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
i.e. a ÷ (2 + 1. 5)
14 ÷ 2 + 1. 5
7+1.5
8.5
This is the way Jayden solved the equation due to which he arrived at the wrong solution.
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The Correct question is as below
Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement.
1. Jayden's solution is incorrect.
2. Jayden added in the parentheses before dividing.
3. Jayden substituted the wrong value for a.
4. Jayden divided 14 by 2 and added 1.5
If point is slid(translated) 4 units to the right, what would the new coordinates be (3,-4)
Aamena buys a business costing $23000
She pays part of this cost with $12000 of her own money
Calculate what percentage of the $23000 this is
Show your calculations
Answer:
52.17%
Step-by-step explanation
[tex]\frac{12000}{23000}[/tex] ×100%
[tex]\frac{1200}{23}[/tex]
52.17
The neck of a gifaffe is 4 1/2 feet in length. Its neck is 30 perocent of it height whats the higet of the giffae
The giraffe is 15 feet tall based on the relation between the length of neck of giraffe and it's height.
Firstly convert the mixed fraction to fraction.
Length of neck of giraffe = (4×2)+1/2
Length of neck = 9/2 feet
Now, let us assume the height of giraffe be x. So, equation will be -
30% × x = 9/2
Rewriting the equation
30/100 × x = 9/2
Cancelling zero
3x/10 = 9/2
Again rewriting the equation
x = 90/6
Performing division on Right Hand Side of the equation
x = 15 feet
Thus, height of giraffe is 15 feet.
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If p and q vary invarsely and p is 11 when q is 28, determine q when p is equal to 4
77 is the value of Q in linear equation.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
P ∝ 1/Q
PQ = K
AT P= 11
Q = 28
11 * 28 = K
K = 308
AT P = 4
4Q = 308
Q = 77
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Write each polynomial in Standard form and name it based on its degree an number of terms.
9x²-213
Standard --
Degree
Terms
We would name this polynomial as a quadratic polynomial with two terms.
In standard mathematics, what is a polynomial function?A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on.
In the standard form of a polynomial, the terms are written in descending order of degree. The standard form for a polynomial of degree n is:
a1x + a0 + anxn + an-1xn-1 +...
We have the polynomial in this case:
9x² - 213
To write it in standard form, rearrange the terms in descending order of degree as follows:
213 + 9x²
As a result, the standard form of the polynomial is:
9x² - 213
This polynomial has degree 2 (because x's highest exponent is 2) and two terms (since there are two distinct parts to the expression, a constant and a term with an x squared coefficient).
As a result, we'd call this polynomial a quadratic polynomial with two terms.
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Find the 8th term of the arithmetic sequence x + 1 x+1, 8 x − 3 8x−3, 15 x − 7 ,
Answer: 50x - 27
Step-by-step explanation:
To find the 8th term of the arithmetic sequence, we need to first find the common difference between consecutive terms:
Common difference (d) = second term - first term
d = (8x - 3) - (x + 1)
d = 7x - 4
Now, we can use the formula to find the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Plugging in the values, we get:
a8 = (x + 1) + (8 - 1)(7x - 4)
a8 = x + 1 + 7(7x - 4)
a8 = x + 1 + 49x - 28
a8 = 50x - 27
Therefore, the 8th term of the arithmetic sequence x + 1, 8x - 3, 15x - 7 is 50x - 27.
a manager recorded the number of gallons of ice cream sold for the past six periods. he asked you to choose a forecasting model to predict the demand for gallons of ice cream in period 7. you consider applying a two-period moving average model and a two-period weighted moving average model with weights of 0.6 and 0.4. a) which model is better for this data set (hint: show all your work including forecasts for each period and calculations using measures of forecast accuracy)? (9 points)
The two-period moving average model and the two-period weighted moving average model are both common forecasting methods used to predict future demand. and we understand that the model with the lower MAD and MSE values will have the most accurate forecast.
To determine which model is better for this particular data set, we need to compare the accuracy of each model. To do this, we will calculate the Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE) for each model.
For the two-period moving average model, we can calculate the forecast for period 7 by taking the average of p5 and 6:
Period 7 forecast = (Gallons in Period 5 + Gallons in Period 6)/2
For the two-period weighted moving average model, we can calculate the forecast for period 7 by using the weights of 0.6 and 0.4:
Period 7 forecast = (0.6 x Gallons in Period 5) + (0.4 x Gallons in Period 6)
We can then compare the accuracy of each model by calculating the MAD and MSE. To calculate MAD, we need to subtract the actual demand in each period from the forecasted demand and take the absolute value:
MAD = |Actual demand – Forecasted demand|
To calculate MSE, we need to square the differences between the actual demand and the forecasted demand:
MSE = (Actual demand – Forecasted demand)^2
After calculating the MAD and MSE for each model, we can compare the results to determine which model is better for this data set. The model with the lower MAD and MSE values will have the most accurate forecast.
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The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59 F and a
standard deviation of 10°F. A random sample of 10 temperatures is taken from the winter months and the mean
temperature is recorded. What is the standard deviation of the sampling distribution of the sample mean for all
possible random samples of size 10 from this population?
The standard deviation of the sampling distribution of the sample mean for the given sample size is equal to 3.1623°F.
For the normally distributed data,
Mean of the population distribution 'μ' = 59F
Population standard deviation 'σ' = 10°F
Sample size 'n' = 10
Formula for the standard deviation of the sampling distribution of the sample mean (also known as the standard error of the mean) is equal to ,
= σ / √(n)
Substitute the value to get the standard deviation of the sampling distribution of the sample mean we get,
= 10°F / √(10)
= 3.1623°F
Therefore, the standard deviation of the sampling distribution of the sample mean for all possible random samples of size 10 from this population is approximately 3.1623°F.
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A man sells an article at rs 600and makes a profit of 20%. Calculate his profit percentage
Answer:
120
Step-by-step explanation:
20 percent of 600 is 120 so he will get 120
suppose 46.37% of all voters in the last election supported the current governor. a telephone survey contacts 328 voters from the last election and asks if they voted for the current governor. what is the probability that at least half of the voters contacted supported the current governor in the last election?
The probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election is 0.0532.
What is the probability?To calculate the probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election, we can use the binomial probability formula.
The formula is: P(x) = (ⁿCₓ) × pˣ × (1-p)⁽ⁿ⁻ˣ⁾
In this case, n = 328, p = 46.37%, and x = 164 (since half of 328 is 164).
Plugging in the numbers we get:
P(x) = ³²⁸C₁₆₄ × (0.4637)¹⁶⁴ × (0.5363)⁽³²⁸⁻¹⁶⁴⁾ = 0.0532
Therefore, the probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election is 0.0532.
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How do you find height when you are doing volume with cubic units?
Answer:calculate the cube root of a cube's volume.
Step-by-step explanation:
which of the following was traditionally an assumption underlying the independent samples t-test question 10 options: a) scores must be drawn from a normally distributed population b) variances should be unequal in both groups c) data should be at the nominal level d)all of the above
The assumption underlying the independent samples t-test is that the scores must be drawn from a normally distributed population. Option A is correct.
What is a t-test?A t-test is a statistical method that determines whether two groups of observations are significantly different from one another. When comparing the means of two populations, the t-test is commonly used. The t-test is used to determine whether two groups' means are significantly different when the samples are drawn from normally distributed populations with equal variances.
The t-test is a powerful tool for determining whether a sample is significantly different from a population or whether two samples are significantly different from one another. The independent samples t-test, as opposed to the dependent samples t-test, is a t-test that compares the means of two independent groups. In this situation, the groups are separate and distinct.
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What geometric shapes can you draw that have exactly one pair of parallel sides? Use pencil and paper. Sketch examples for as many different types of shapes as you can. Use appropriate marks to show the pairs of parallel sides.
A. regular pentagon
B. square
C. Trapezoid
D. parallelogram
what is the sum of all integer values of $x$ such that $\frac{31}{90} < \frac{x}{100} < \frac{41}{110}$ is true?
Kate plans to save 5% of her income. She just earned 80.Howmuchmoneyshouldsheputintosavings?
$4
Multiply 80 by 0.05 to get the answer of $4
Answer:
4 (insert the currency needed)
Step-by-step explanation:
To find our answer we have to find 5% of Kate's wages and to do this we have to do 5 divided by 100. Then that answer is multiplied by 80!
5 ÷ 100 = 0.0580 × 0.05 = 4This means she has to put £4 into her savings!
Hope this helps, have a lovely day! :)
Find the area of the cicumfrance of a circle with diameter of 5ft use 3.14 for pi
Step-by-step explanation:
The formula to solve for the area of a circle is given by,
A
=
1
4
π
d
2
where
d
is the diameter.
Substituting the given, we have
A
=
1
4
×
3.14
×
(
3
ft
)
2
=
1
4
×
3.14
×
9
ft
2
A
=
7.065
ft
2
Next, solve for the circumference.
The formula for the circumference of a circle is written as,
C
=
π
d
where
d
is the diameter.
Substituting the given, we have
C
=
3.14
×
3
ft
C
=
9.42
ft
Hence, the
Area
=
7.065
ft
2
and the
Circumference
=
9.42
ft
.
Answer:
A = 19.625 ft²
C = 15.7 ft
Step-by-step explanation:
The equation for the area of a circle is πr², where r is the radius.
The radius is half of the diameter, so the radius here is 2.5.
Plug the radius into the equation and substitute 3.14 for π:
A = 3.14 x 2.5²
2.5² = 2.5 x 2.5 = 6.25
A = 3.14 x 6.25 = 19.625
Area = 19.625 ft²
The equation for the circumference of a circle is 2πr.
Plug the radius into the equation and substitute 3.14 for π:
C = 2 x 3.14 x 2.5
C = 15.7
Circumference = 15.7 feet.
In order to make the same amount of money, they would have to each sell ______ bicycles. They would both make $______.
In order to make the same amount of money, they would have to each sell 5 bicycles. They would both make $500
How many bicycle would they sell to make the same amount of money?To find the number of bicycles they would need to sell to make the same amount of money,
We can set Jim's and Tom's weekly earnings equal to each other and solve for the number of bicycles:
250 + 50x = 400 + 20x
30x = 150
x = 5
So they would need to sell 5 bicycles to make the same amount of money.
How much would they make for selling that amountTo find out how much money they would make for selling 5 bicycles, we can substitute x = 5 into either equation.
Let's use Jim's equation:
250 + 50(5) = 500
So they would make $500 for selling 5 bicycles.
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Work out the fraction and ratio that
complete the equations below.
Give each answer in its simplest form.
a) h:k=5:6
h =
k
b) 2x=9y
x:y
=
:
The fraction and ratio that complete the equations in its simplest term is 5/6k and 2 : 9 respectively.
What is the fraction and ratio that complete the equations?h : k = 5 : 6
h/k = 5/6
cross product
h × 6 = k × 5
6h = 5k
divide both sides by 6
h = 5/6k
Then,
2x = 9y
2/9 = x/y
2 : 9 = x : y
Ultimately, the simplest form of fraction and ratio which completes the equation is 5/6k and 2:9.
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Find a basis for the space of 2x2 lower triangular matrices:
A basis for the space of 2x2 lower triangular matrices is [tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex].
Lower triangular matrices resemble the following:
[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right][/tex]
We can write it like this:
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right][/tex]
This demonstrates the set's
[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]
covers the set of lower triangular matrices with dimensions 2x2. Moreover, these are linearly independent, so attempting to
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
leads to
[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right] =\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
which results in a = b = c = 0 right away. As there is no other way to
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
, these matrices are linearly independent if a = b = c = 0.
Since
[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]
they serve as a foundation by spanning the collection of 2x2 lower triangular matrices and being linearly independent.
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