Respuesta :
Answer:
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)
