1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
grandymaker [24]
1 year ago
13

10. (a) Consider the following matrices: A = ( 2 ) B = (3) and C = (-3) w = Find the det(A). [1] (ii) Is the matrix A singular?

Justify your answer. [1] (iii) Suppose the AB = C. Determine the values of x and y. [3] (iv) Is it possible to find the matrix product BA? State why or why not. [2]

Mathematics
1 answer:
Viefleur [7K]1 year ago
6 0

i) We have to find the determinant of A.

We can do this as:

\det(A)=|\begin{bmatrix}{3} & {6} \\ {1} & {-2}\end{bmatrix}|=3*(-2)-6*1=-6-6=-12

ii) We have to find if the matrix A is singular.

Singular matrix have determinant equal to 0.

This is not the case for A, as its determinant is -12. Then, A is not a singular matrix.

iii) We have to find the values of x and y so that AB = C.

We have to write the matrix multiplication and we will obtain a system of linear equations:

We can now solve the system of equations by adding 3 times the second equation to the first equation:

\begin{gathered} 3(x-2y)+(3x+6y)=3(-3)+(-3) \\ 3x-6y+3x+6y=-9-3 \\ 6x+0y=-12 \\ x=\frac{-12}{6} \\ x=-2 \end{gathered}

We can now use the second equation to find the value of y:

\begin{gathered} x-2y=-3 \\ x+3=2y \\ y=\frac{x+3}{2} \\ y=\frac{-2+3}{2} \\ y=\frac{1}{2} \end{gathered}

The values are x = -2 and y = 1/2.

iv) When we want to multiply two matrices, the required condition is that the number of columns of the matrix on the left is equal the number of rows of the matrix on the right.

In the case of A(2x2) and B(2x1), when we do A*B this condition is satisfied.

But when we try to multiply BA, the number of columns of B is not equal to the number of rows of A, so the matrix mulitplication is not possible.

Answer:

i) det(A) = -12

ii) A is not singular because singular matrices have determinant equal to zero.

iii) x = -2 and y = 1/2.

iv) Is not possible because the number of columns of the first matrix has to be equal to the number of rows of the second matrix.

You might be interested in
How do you do the last two questions?
Mashutka [201]

Answer:

P = 6200 / (1 + 5.2e^(0.0013t))

increases the fastest

Step-by-step explanation:

dP/dt = 0.0013 P (1 − P/6200)

Separate the variables.

dP / [P (1 − P/6200)] = 0.0013 dt

Multiply the left side by 6200 / 6200.

6200 dP / [P (6200 − P)] = 0.0013 dt

Factor P from the denominator.

6200 dP / [P² (6200/P − 1)] = 0.0013 dt

(6200/P²) dP / (6200/P − 1) = 0.0013 dt

Integrate.

ln│6200/P − 1│= 0.0013t + C

Solve for P.

6200/P − 1 = Ce^(0.0013t)

6200/P = 1 + Ce^(0.0013t)

P = 6200 / (1 + Ce^(0.0013t))

At t = 0, P = 1000.

1000 = 6200 / (1 + C)

1 + C = 6.2

C = 5.2

P = 6200 / (1 + 5.2e^(0.0013t))

You need to change the exponent from negative to positive.

The inflection points are where the population increases the fastest.

5 0
3 years ago
The total number of miles Jeremy walked on a hike can be represented by using the formula. If and n represents the total number
KatRina [158]

Answer:

A) 2 miles, 5 miles, 8 miles

Step-by-step explanation:

Let's get some details cleared.

We're interested in finding how many miles he walked at the end of each hour in a period of 3 hours.

We know what  is, so we can use that as our starting point.

Your answer is A.

7 0
3 years ago
Read 2 more answers
A physical trainer decides to collect data to see if people are actually weight changing weight during the shelter in place. He
telo118 [61]

Answer:

H0: µd = 0 (claim)

H1: µd ≠ 0

This is a two-tail t-test for µd

Step-by-step explanation:

This is a paired (dependent) sample test, with its hypothesis is written as :

H0: µd = 0

H1: µd ≠ 0

From the equality sign used in the hypothesis declaration, a not equal to ≠ sign in the alternative hypothesis is used for a two tailed t test

The data isn't attached, however bce the test statistic cannot be obtained. However, the test statistic formular for a paired sample is given as :

T = dbar / (Sd/√n)

dbar = mean of the difference ; Sd = standard deviation of the difference.

3 0
3 years ago
The correct answer please.​
11Alexandr11 [23.1K]
Y+4= -4(x-3)
y+4=-4x+12
4x+y=8
7 0
3 years ago
Read 2 more answers
What is the percent increase when 7,200 increases by 1,800?
Nuetrik [128]

Answer:

B.

Step-by-step explanation:

The percent increase when 7200 increases by 1800 is 25 %

8 0
2 years ago
Read 2 more answers
Other questions:
  • John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70. Which inequality w
    7·2 answers
  • What would be the answer? Or how do I solve it?
    7·1 answer
  • If x is 5, then 6x =
    8·2 answers
  • What value of x is in the solution set of 2(3x - 1) 24 - 6?
    10·1 answer
  • Help me find the volume please!
    6·1 answer
  • Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?
    15·1 answer
  • Which set of three numbers can be used to make a right triangle?
    10·2 answers
  • What is the linear equation of a line with a rate of change of −1/2 that passes through the point (0,4)?
    11·2 answers
  • Please help pleasehelp
    6·1 answer
  • Determine which of the following statements is NOT correct. 00:00 The equation x + 1.793 = 2.42 can be rewritten as x-1.793 = 2.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!