Answer to Question #101845 in Matrix | Tensor Analysis for kelbesa Gemechu

Question #101845
Suppose A is a square matrix such that det(A0 = 2 and det(3A the power of t) = 18 then find the order of matrix A
1
Expert's answer
2020-02-11T10:35:56-0500

Suppose AMn​(R).

Then, 

"\\det (3A^t) = 3^n\\det(A^t) = 3^n\\det(A^t) =3^n\\det(A)="

"=2 \\cdot 3^n=18"

because the determinant is multilinear as a function of rows and the determinant respects the matrix multiplication. We have, then,

"3^n=9,"

which implies that  "n=2."

The solution relies on the assumption that t∈Z because "A^t" might not be defined otherwise.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS