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

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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.

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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,

                   

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