Use MATLAB to compute the determinants of the matrices A+B, A-B, AB, A-1, and BT. (Recall that in MATLAB, BT is written as B'.) Which of the above matrices are not invertible? Explain your reasoning. Suppose that you didn't know the entries of A and B, but you did know their determinants. Which of the above determinants would you still be able to compute from this information, even without having A or B at hand? Explain your reasoning.

The problem is solved in Matlab and the code with explanation is provided below.

Explanation:

(a) Use MATLAB to compute the determinants of the matrices A+B, A-B, AB, A⁻¹, and BT

We can use the Matlab function det() to calculate the determinants and inv() function is used to calculate the inverse.

A = [8 11 2 8; 0 -7 2 -1; -3 -7 2 1; 1 1 2 4]

B = [1 -2 0 5; 0 7 1 5; 0 4 4 0; 0 0 0 2]

a=det(A+B)

b=det(A-B)

c=det(A*B)

d=det(inv(A))

e=det(B')

Output:

A =

    8    11     2     8

    0    -7     2    -1

   -3    -7     2     1

    1     1     2     4

B =

    1    -2     0     5

    0     7     1     5

    0     4     4     0

    0     0     0     2

a =    4.4964e-15 (this is basically zero)

b =    1.0380e+03

c =     3648

d =    0.0132

e =    48

(b) Which of the above matrices are not invertible? Explain your reasoning

As you can see in part (a) the determinant of A+B is approximately zero  and we know that the determinant of an invertible matrix can never be zero hence A+B must  be non-invertible.

(c) Suppose that you didn't know the entries of A and B, but you did know their determinants. Which of the above determinants would you still be able to compute from this information, even without having A or B at hand? Explain your reasoning.

If we did not had original matrix A and B but we had det(A) and det(B) then we could have found  the following by using the properties of determinants:

1. A*B because det(A)*det(B) = det(A*B)

2. inv(A) because inv(A) = 1/det(A)

3. B' because det(B') = det(B)

your game would probably crash if its too much lag but other players will also ! xd

hope this ! xd

also, can i get brainliest ?

the best that can be interferred in this except is that molina has taken up the cause of abused and disadvantaged kids through his foundation. and that the chance to live up to clemente's legacy was a motivating factor for him to continue defending those who are in an unfavourable possition.