Solution Found!
a. If C is the cofactor matrix of A, give a formula for det C in terms of det A. b. Let
Chapter 5, Problem 12(choose chapter or problem)
a. If C is the cofactor matrix of A, give a formula for det C in terms of det A.
b. Let \(C=\left[\begin{array}{rrr} 1 & -1 & 2 \\ 0 & 3 & 1 \\ -1 & 0 & -1 \end{array}\right]\) Can there be a matrix A with cofactor matrix C and det A = 3? Find a matrix A with positive determinant and cofactor matrix C.
Questions & Answers
QUESTION:
a. If C is the cofactor matrix of A, give a formula for det C in terms of det A.
b. Let \(C=\left[\begin{array}{rrr} 1 & -1 & 2 \\ 0 & 3 & 1 \\ -1 & 0 & -1 \end{array}\right]\) Can there be a matrix A with cofactor matrix C and det A = 3? Find a matrix A with positive determinant and cofactor matrix C.
ANSWER:Step 1 of 6
a) Let be the cofactors of respectively for .
Then,