- #1
shiri
- 85
- 0
Let A, B and C be 3x3 invertible matrices where det(A)=4 , det(B)=4 and det(C) is some non-zero scalar.
a) det [(C^T)(A^-1)(B^2)(C^-1)]
b) det [-2(A^2)^T(C^2)(B^-1)(C^-1)^2]
a)
What I got is:
det [(A^-1)(B^2)(C^T)(C^-1)]
= det [(A^-1)(B^2)(C)(C^-1)]
= det [(A^-1)(B^2)]
= [1/det(A)]*[det(B)]^2
= (1/4)*(4)^2
= 16/4
= 4
b)
What I got is:
det [-2(A^2)^T(B^-1)(C^2)(C^-1)^2]
= (-2)^3 det [(A^2)^T(B^-1)(C^2)(C^-2)]
= -8 det [(A^2)(B^-1)]
= -8 [det(A)]^2*[1/det(B)]
= -8 (4)^2*(1/4)
= -8 (16)*(1/4)
= -8*4
= -32
Can anyone please tell me, am I getting the right answers for a) and b)?
a) det [(C^T)(A^-1)(B^2)(C^-1)]
b) det [-2(A^2)^T(C^2)(B^-1)(C^-1)^2]
a)
What I got is:
det [(A^-1)(B^2)(C^T)(C^-1)]
= det [(A^-1)(B^2)(C)(C^-1)]
= det [(A^-1)(B^2)]
= [1/det(A)]*[det(B)]^2
= (1/4)*(4)^2
= 16/4
= 4
b)
What I got is:
det [-2(A^2)^T(B^-1)(C^2)(C^-1)^2]
= (-2)^3 det [(A^2)^T(B^-1)(C^2)(C^-2)]
= -8 det [(A^2)(B^-1)]
= -8 [det(A)]^2*[1/det(B)]
= -8 (4)^2*(1/4)
= -8 (16)*(1/4)
= -8*4
= -32
Can anyone please tell me, am I getting the right answers for a) and b)?