a. An n × n determinant is defined by determinants of

Chapter 3, Problem 39E

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QUESTION:

In Exercises 39 and 40, A is an \(n \times n\) matrix. Mark each statement True or False. Justify each answer.

a. An \(n \times n\) determinant is defined by determinants of \((n-1) \times(n-1)\) submatrices.

b. The (i; j)-cofactor of a matrix A is the matrix \(A_{i j}\) obtained by deleting from A its ith row and j th column

Questions & Answers

QUESTION:

In Exercises 39 and 40, A is an \(n \times n\) matrix. Mark each statement True or False. Justify each answer.

a. An \(n \times n\) determinant is defined by determinants of \((n-1) \times(n-1)\) submatrices.

b. The (i; j)-cofactor of a matrix A is the matrix \(A_{i j}\) obtained by deleting from A its ith row and j th column

ANSWER:

Solution 39E

(a) The statement “A   matrix determinant is defined by determinants of (

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