Explanation Approach: Follow the below mentioned statement to find the minors of the given matrix. If A is a square matrix, then the minor M i j of the entry a i j is the determinant of the matrix obtained by deleting the i th row and j th column. The method to find the determinant of a square matrices of dimension n × n is as follows, If A is a square matrix (of dimension 2 × 2 or greater), then the determinant of A is the sum of the entries in any row (or column) of A multiplied by their respective cofactors. For example, expanding along the first row yields as shown below. | A | = a 11 C 11 + a 12 C 12 + ⋯ + a 1 n C 1 n The cofactors of the given square matrix can be calculated by the formula, C i j = ( − 1 ) i + j M i j Calculation: Consider the given matrix, A = [ 1 4 − 2 3 2 0 − 1 4 3 ] In above matrix the one of entry in the second row is zero. So to eliminate some of the work in the expansion, expand along the second row. | A | = 3 ( C 21 ) + 2 ( C 22 ) + 0 ( C 23 ) … ( 1 ) Here, the cofactors C 23 has zero coefficient, so the only cofactors need to find are C 21 , C 22 . Consider the formula to find the cofactors of the square matrix, C i j = ( − 1 ) i + j M i j Apply the formula of cofactors to find the cofactor C 21

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ISBN: 9781337271073

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 8.4, Problem 51E

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The determinant of the matrix [14−2320−143] and expand by cofactors using the row or column that is easy to compute.

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Chapter 8.4, Problem 50E

Chapter 8.4, Problem 52E

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Ch. 8.1 - Prob. 1CP Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 5CP Ch. 8.1 - Prob. 6CP Ch. 8.1 - Prob. 7CP Ch. 8.1 - Prob. 8CP Ch. 8.1 - Prob. 9CP Ch. 8.1 - Prob. 1E

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The determinant of the matrix [ 1 4 − 2 3 2 0 − 1 4 3 ] and expand by cofactors using the row or column that is easy to compute.

Solution Summary: The author explains how to find the determinant of a square matrices of dimension ntimes.

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To find:

The determinant of the matrix [14−2320−143] and expand by cofactors using the row or column that is easy to compute.

Want to see the full answer?

Chapter 8 Solutions

The determinant of the matrix [ 1 4 − 2 3 2 0 − 1 4 3 ] and expand by cofactors using the row or column that is easy to compute.

Solution Summary: The author explains how to find the determinant of a square matrices of dimension ntimes.

Videos

To find: The determinant of the matrix [14−2320−143] and expand by cofactors using the row or column that is easy to compute.

Want to see the full answer?

Chapter 8 Solutions

To find:

The determinant of the matrix [14−2320−143] and expand by cofactors using the row or column that is easy to compute.