Use row-reduction to compute the inverse of the matrix below, if it exists, and confirm your answer by comparison with the formula [ : :] = if ad-bc70. ad-bc cd -C a 7 1 4 5 Set up the correct augmented matrix needed in order to find the inverse by row-reduction. 7 4 5 (Type integers or simplified fractions.)
Answers
The inverse of the matrix A is [ -1/5 8/5 -7/5; -2/5 9/5 -7/5; -1/5 2/5 3/5 ].
The given matrix is A = [7 4 5, 1 -2 3, -1 3 -2].To find the inverse of the matrix A, we need to use the augmented matrix A|I, where I is the 3x3 identity matrix.
Hence, the augmented matrix will be [7 4 5 1 0 0, 1 -2 3 0 1 0, -1 3 -2 0 0 1].To find the inverse of the matrix, we reduce the left-hand side of the augmented matrix to the identity matrix by performing row operations on the augmented matrix until the left-hand side is the identity matrix.
If the left-hand side of the augmented matrix is reduced to the identity matrix, then the right-hand side of the augmented matrix is the inverse of the original matrix.
Let's perform the row operations on the augmented matrix to get the inverse of matrix A as shown below: 7 4 5 1 0 0 -1/5 8/5 -7/5 1/5 0 0 1 -2 3 0 1 0 -2/5 9/5 -7/5 0 1 0 -1 3 -2 0 0 1 -1/5 2/5 3/5 0 0 1
To verify the correctness of the inverse, we use the formula [A][A⁻¹] = [A⁻¹][A] = [I], where I is the identity matrix.
On computing the products of the matrix [A][A⁻¹] and [A⁻¹][A], we get the 3x3 identity matrix.
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Related Questions
onsider the following production function: y = F(L, K) = 4L3 K} = where L and K are the amount of labour and capital used in the production process, and y is the output. Throughout this question, the output price p is 3 and the rental rate of capital r is 1. We will first consider a firm in the short run, where the amount of capital is fixed at K = 64. The fixed cost is therefore 64. = (a) (Level A) Is there diminishing returns to labour? Explain. (b) (Level A) Suppose the wage rate w is 1. Find the profit-maximising choice of L. Calculate the profit-maximising output level and the maximised profit. (There is no need to check the second order condition but of course you can check if you want to.) (c) (Level A) Now suppose w increases to 2. Find the profit-maximising choice of L. Calculate the profit-maximising output level and the maximised profit. (There is no need to check the second order condition.) You can leave your answers in square roots. (d) (Level A) What is the change in L when w increases from 1 to 2 in the short run? You can leave your answers in square roots.
Answers
Yes, there are diminishing returns to labor in the given production function.
What is the profit-maximizing choice of labor and the resulting output and profit level when the wage rate is 1?
There are diminishing returns to labor in the given production function. As more units of labor (L) are added while holding capital (K) constant, the increase in output (y) becomes smaller and smaller. This is indicative of diminishing marginal product of labor.
When the wage rate (w) is 1 and the capital (K) is fixed at 64, the profit-maximizing choice of labor (L) can be found by equating the marginal product of labor (MPL) to the wage rate. In this case, MPL = 12L^2K.
Setting MPL = w, we have 12L^2K = 1. Substituting K = 64, we get 12L^2 * 64 = 1. Solving for L, we find L ≈ 0.0917.
The profit-maximizing output level (y) can be calculated by substituting the values of L and K into the production function. Thus, y = 4L^3K = 4(0.0917)^3 * 64 ≈ 0.026.
The maximized profit can be determined by subtracting the total cost (TC) from the total revenue (TR). Since the fixed cost is given as 64, TC = 64 + wL = 64 + 1(0.0917) ≈ 64.092. TR is the product of the output level and the price, which is 0.026 * 3 = 0.078.
Profit = TR - TC ≈ 0.078 - 64.092 ≈ -63.014.
Diminishing returns to labor imply that as more labour is employed while holding other factors constant, the incremental increase in output becomes smaller. In the given production function, this phenomenon is observed. In the short run, with a fixed capital level of 64, we determine the profit-maximizing choice of labour (L) when the wage rate (w) is 1. By equating the marginal product of labour (MPL) to the wage rate, we find L ≈ 0.0917. Substituting this value into the production function, we calculate the profit-maximizing output level as y ≈ 0.026. The maximized profit is determined by subtracting the total cost (TC) from the total revenue (TR), resulting in a profit of approximately -63.014. This analysis helps understand the relationship between input choices, output levels, and profit optimization in the short run.
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21 containers in total hold 200 balls. Prove that at least 2 boxes must contain the same number of balls.
You must show all steps clearly.
Hint: use contradiction.
Answers
The assumption that there is no box with the same number of balls must be false. Therefore, at least 2 boxes must contain the same number of balls.
Let's assume that there is no box with the same number of balls. Then each container has a different number of balls. To get a maximum number of balls, we begin by putting 1 ball in the first container, 2 in the second, 3 in the third, and so on up to the 21st container. This yields a total of 1+2+3+4+...+20+21 = 21*(21+1)/2 = 231 balls.
We cannot have more than this because each container can hold at most one ball more than the last. Now we take out 31 balls. There are still 200 balls remaining. Because each container has a different number of balls, we can place one ball in each of the first 21 containers, yielding a total of 21 balls. Then we can place one ball in each of the first 11 containers, yielding a total of 11 more balls, for a total of 32 balls. The remainder is 200-32=168 balls.
Because each of the first 11 containers has one ball, each of the remaining 10 containers must have at least 1 ball. Thus, the total number of balls remaining is at least 10+1+1+...+1 (10 times) = 20.
This gives us a total of 32+20=52 balls. This is less than the 69 balls remaining. Therefore, the assumption that there is no box with the same number of balls must be false. Therefore, at least 2 boxes must contain the same number of balls.
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(a + y)2 + 2y if a = 5 and y = -3.
Answers
Answer:
-2
Step-by-step explanation:
Plug in the values and solve
4. Write an equation that relates the measure of
Answers
Answer:
2x - 8 = 50
Step-by-step explanation:
∠ CBD and ∠ ABE are vertically opposite angles and are congruent , then
2x - 8 = 50
6 The manufacturer of an oven states that the
temperatures displayed while cooking are within a
5% error. Rachel is using the oven to cook a chocolate
cake that must be cooked at a temperature below
325°C. The oven display shows a temperature of 310°C.
Can Rachel be certain that the temperature is suitable
for cooking her cake? Explain your answer.
Answers
Result, Rachel can be certain that the temperature is suitable for her cake.
Rachel cannot be certain that the temperature displayed on the oven is suitable for cooking her cake.
The manufacturer's claim of a 5% error on the displayed temperature means that the actual oven temperature can be off by 5% in either direction. To calculate the range of possible actual temperatures, we need to find 5% of 310°C. 5% of 310 = (5/100) * 310 = 15.5°C This means that the oven temperature could be 15.5°C higher or 15.5°C lower than the displayed temperature.
To find the maximum possible temperature, we add the error to the displayed temperature: 310°C + 15.5°C = 325.5°C Since the maximum possible temperature is slightly above 325°C, Rachel cannot be certain that the temperature is suitable for cooking her cake, as it needs to be cooked at a temperature below 325°C. It's important for Rachel to consider using an alternative thermometer or verifying the actual temperature with the oven manufacturer to ensure the cake is cooked at the desired temperature.
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When finding the margin of error for the mean of a normally distributed population from a sample, what is alpha, assuming a confidence level of 74%? 0.13 0.26 0.74 0.87
Answers
The margin of error when the confidence level of 74% is 0.26. Then the correct option is B.
What is the margin of error?The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.
The mean of a normally distributed population from a sample.
The confidence level of 74%.
Then the margin of error is given as
Margin of error = 1 – α
Margin of error = 1 – 0.74
Margin of error = 0.26
The margin of error when the confidence level of 74% is 0.26. Then the correct option is B.
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Answer:
0.26 or B
Step-by-step explanation:
HELP
ME
I WILL BLESS YOU
Answers
Answer:
I believe the volume would be 3.75 or 3 and 3/4
Step-by-step explanation:
To get the volume you have to multiply Length×width×height
The length is 5/2 (2.5)
The width is 1
The height is 3/2 (1.5)
2.5×1= 2.5
2.5×1.5=3.75 or 3 3/4
5/4 = equals what like I need an answer
Answers
In decimal form, 5/4 is equal to 1.25
Answer:
5 divided 4 = 1.25. 4 divided 5 = 0.8.
Step-by-step explanation:
is the relation a function?
Answers
Hope this helps
Have a great day/night
Solve for x. Round your answer to the nearest hundredth.
Answers
Step-by-step explanation:
sin 53° = x/26
0.7986 = x/26
=> x = 26×0.7986
= 20.76
Tan 39° = 52/x
0.8098 = 52/x
=> x = 52/0.8098
= 64.21
cos x = 7/15 = 0.4667
x= arc cos 0.4667 = 62.18°
sin x = 27/46 = 0.5870
x = arc sin 0.5870 =35.94°
In order to isolate the variable term in the equation 6 -2x = -3 using the subtraction property of equality, which number
should be subtracted from both sides of the equation?
-3
-2
3
6
Answers
Answer:
6
Step-by-step explanation:
The reason you would do 6 is because you need to isolate the variable term.
This means you need the variable and its coefficient alone. so if you subtract 6 from each side of the equation you can achieve that goal. So the equation would then read -2x= -9 (because you combine the like terms of -6 and the -3 that was already there)
If you need to complete the rest of the equation you would divide both sides by -2 to further isolate x. This means x= 9/2 (since they are both negative they cancel each other out turning it positive) and the simplified answer would be 4 1/2
Hope this helps <3
A box of cereal costs $1.92 for 16 ounces. At that rate, how much would a 40-ounce box of cereal cost?
Answers
Find cost per ounce:
1.92 / 16 = 0.12 per ounce
0.12 x 40 = 4.80
The answer is $4.80
Answer:
$4.8
Step-by-step explanation:
In order to find the answer, you would need to divide $1.92 by 16 ounces to get how much cereal it costs for one ounce which is $0.12. After that, you would need to multiply $0.12 times 40 which would equal $4.8
Hope this helps and have a great day:)
Can someone help me find the x
Answers
can you tell me what your doing here and might help.
Answer:
4
Step-by-step explanation:
A rectangular garden has a length of 100 metres and a width of 50 metres. A
square swimming pool is to be constructed inside the garden. Find the length of
one side of the swimming pool if the remaining area (not occupied by the pool)
is equal to one half the area of the rectangular garden.
Answers
Answer:
50 by 50 meter pool
Step-by-step explanation:
since a 100 by 100 meter pool won’t fit the only option is a 50 by 50 meter pool
100x50=5000
5000/2=2500
50x50=2500
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Emily has $40 in a savings account that earns 10% interest, compounded annually.
To the nearest cent, how much interest will she earn in 2 years?
Answers
Answer:
$48.
Step-by-step explanation:
Annual means yearly.
The question is asking how much will Emma earn after 10% interest for 2 years.
To solve:
Find 120% of $40. This represents 100% (40) and 20% interest for the 2 years.
Round to the nearest cent if it's necessary.
Let's solve:
Let's find 20% of $40 first.
Divide 40 by 5:
$8 is 20% of 40.
Add 8 to 40:
8 + 40
= 48.
48 is your answer.
*48 represents 10% interest for 2 years.
Earl earned $356 in gross pay. He had
$27.23 deducted for FICA taxes and $52.69
deducted for state and federal taxes. What
percent of his gross pay did he take home?
Answers
Answer:
77.5506% I believe is the answer unrounded.
77.55% rounded to the nearest hundredth.
77.6% rounded to the nearest tenth.
Step-by-step explanation:
356 = 100%
(356 - 27.23) - 52.69
328.77 - 52.69
276.08
what does democracy mean and how do we practice it in the United States of America PLEASE HELPPP!!!!
Answers
Answer:
a system of government by the whole population or all the eligible members of a state, typically through elected representatives. The United States is one of the world's developed democracies where third parties have the least political influence. The federal entity created by the U.S. Constitution is the dominant feature of the American governmental system.
Step-by-step explanation:
What fraction goes in the box to make it correct?4×□=1
Answers
Answer:
1/4
4 × .25 = 1
An episode of a television show is 60 minutes long when it originally airs with commercials. On a DVD without commercials, the episode is only 41 1/2 minutes long. How many 1/2 minute commercials did the episode include when it originally aired? Enter and solve an equation to justify your answer.The equation blank + Blankc = blank models the problem, where c is the number of commercials. The episode included blank 1/2 commercials.
Answers
The episode with commercials consists of 60 minutes, and without those, it consists of 41.5minutes; therefore, 60-41.5=18.5 minutes are only commercials when the episode airs.
Divide those 18.5minutes into intervals of 0.5 minutes by calculating
\(\frac{18.5}{0.5}=37\)Therefore, the equation is
\(\begin{gathered} 41.5+0.5c=60 \\ \end{gathered}\)Solving for c,
\(\Rightarrow c=\frac{18.5}{0.5}=37\)Then, the episode included 37 1/2-minute commercials.
HELP ME ASAP PLS!!
PLUMBING Salvatore is a plumber. He charges $100 for all work that is completed in less than 2 hours. He charges $250 for work that requires 2
to 5 hours, and he charges $400 for work that takes between 5 and 8 hours.
Which best describes the domain of the function that models Salvatore's price scale?
O A) The domain is {100, 150, 400}.
OB) The domain is {z 0 < x < 8}.
C) The domain is {z 100 < x < 400}.
OD) The domain is {zz = 2, 5, 8}.
Answers
The domain of the function that models Salvatore's price scale is; {x 0 < x < 8}.
What is the Domain of the Inequality?The domain of a graph is defined as the set of possible input values of a function.
Now, we are told that he charges $100 for all work that is completed in less than 2 hours and also that he charges $400 for work that takes between 5 and 8 hours.
This means that the number of hours will be less than 2 but cannot be zero but it is less than or equal to 8
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please help me!?))),)$&$(
Answers
Answer:
Put a point at -5 on the Y axis.
Then move up 6 (still on the Y axis)
Then move to the right 1 (this should be the point 1,1 on the graph)
Draw a line through the points
Shade to the right of the line you drew
Original equation:
3(a-2) + 14 =8-6a
Solution: 3a-2+14-8-6a
3a +12=8-6a
9a + 12 = 8
9a = -4
a = -4/9
Answers
so what do you need help with
answer me step by step
if don't I will report you
Answers
Explain
Area of 4 congruent parallelograms= 308cm^2
Area of 1 parallelogram = 308/ 4
Area of 1 parallelogram = 77 cm ^2
h+h= 14
As h+h=2h
2h=14
Divide both side by by 2
H= 7
Solve for b
As b+b = 2b
2b+6=y
Subtract both side by 6
2b+6-6=y-6
Combining numbers
2b=y-6
Divide both side by 2
2b/2 = y-6/2
Cancel 2
B= y-6/2
We have of 1 parallelogram = 77 cm^2
H= 7
B= y-6/2
Parallelogram area = bh
So now parallelogram area = y-6/2 x7
And area of 1 parallelogram = 77 cm^2
Y-6/ 2 x 7 = 77
Y-6/2 x 7= 7(11)
Cancel 7
Y-6/2 = 11
Multiple both by 2
2(y-6/ 2) = 11x2
Cancel 2 and multiple numbers
Y-6=22
Add 6 both sides
Y-6+6=22+6
Y=28
2. A parallelogram must be a rhombus when its (2 pts)
(1) diagonals are perpendicular
(2) diagonals are congruent
(3) opposite sides are parallel
(4) opposite sides are congruent
Answers
A parallelogram must be a rhombus when its diagonals are perpendicular.
What is a rhombus?A rhombus is a quadrilateral that has all its four sides equal in length. The diagonals of the rhombus bisect each other at a right angle. Also, the opposite angles of a rhombus are equal in measure and opposite sides are parallel to each other.
Given that, a parallelogram is a rhombus,
According to the definition of a rhombus, we know that, The diagonals of the rhombus bisect each other at a right angle.
Hence, the true statement is A parallelogram must be a rhombus when its diagonals are perpendicular.
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Which statement is TRUE for a chemical change?
A
The identity of the substance does not change.
B
The mass is conserved.
C
The substance always changes from solid to liquid.
D
The particles are not rearranged.
Answers
Answer:
B. The mass is conserved
Step-by-step explanation:
A. The identity of the substance does not change. [FALSE]
B. The mass is conserved. [TRUE]
C. The substance always changes from solid to liquid. [FALSE]
D. The particles are not rearranged. [FALSE]
Melanie invested $3,800 in an account paying an interest rate of 2% compounded
quarterly. Sebastian invested $3,800 in an account paying an interest rate of 2%
compounded monthly. After 6 years, how much more money would Sebastian have in
his account than Melanie, to the nearest dollar?
Answers
Answer:
101
Step-by-step explanation:
Answer:101
Step-by-step explanation:
Given: 9x>-36.
Choose the solution set.
O [xlx>-4)
O'{x1x<-4}
O [xlx>4)
O [xlx<4)
Answers
[x | x > -4)
This can be read as "the set of all x such that x is greater than -4."
Increase £2193.67 by 18.5% Give your answer rounded to 2 DP.
Answers
Then 0.1% x 5
Then times by 2193.67
a basket of fruits contains 5 apples and 3 pears. sharon took two fruits at random. what is the probability that both fruits are apples? write your answer in the simplest form of fraction
Answers
The probability that Sharon randomly selects two apples from the basket of fruits, given that there are 5 apples and 3 pears, can be expressed as a fraction.
To find the probability, we need to consider the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the number of ways Sharon can select any two fruits from the basket, which can be calculated using combinations. In this case, there are 8 fruits in total, so the total number of possible outcomes is C(8, 2) = 28.
The number of favorable outcomes is the number of ways Sharon can select two apples from the five available in the basket, which is C(5, 2) = 10.
Therefore, the probability that both fruits Sharon selects are apples is 10/28, which can be simplified to 5/14.
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Subtract 6 1/3 - 2 1/5
Answers
Answer:
4 2/15
Step-by-step explanation:
Convert both fractions to have the same denominator. Find the LCM of 3 and 5 and multiply by what you need to get there. 1x5=5, 3x5=15, so 1/3 becomes 5/15, and 1x3=3, 5x3=15, so 1/5 becomes 3/15. Finally, do normal subtraction, to get 4 2/15.