Explanation Given: The given matrix is, A = [ 1 2 3 0 − 1 5 2 1 4 ] 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 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 The sign patterns of the cofactors are as follows, The odd positions where i + j is odd, have negative signs. The even position where i + j is even, have positive signs. Calculation: Consider the given matrix, A = [ 1 2 3 0 − 1 5 2 1 4 ] To find the minor M 11 , delete the first row and the first column of A and find the resulting matrix. M 11 = | − 1 5 1 4 | = − 1 × 4 − 1 × 5 = − 4 − 5 = − 9 Similarly, to find the M 12 , delete the first row and second column. M 12 = | 0 5 2 4 | = 0 × 4 − 2 × 5 = 0 − 10 = − 10 Similarly, to find the M 13 , delete the first row and third column. M 13 = | 0 − 1 2 1 | = 0 × 1 − 2 × ( − 1 ) = 0 + 2 = 2 Continuously follow this pattern and obtain the other minors. M 21 = 5 M 22 = − 2 M 23 = − 3 M 31 = 13 M 32 = 5 M 33 = − 1 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 and substitute the suitable value of minors to find the cofactor C 11

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Chapter 8.4, Problem 2CP

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The all minors and cofactors of the given matrix A=[1230−15214].

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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 all minors and cofactors of the given matrix A = [ 1 2 3 0 − 1 5 2 1 4 ] .

Solution Summary: The author explains how to find the minors and cofactors of the given matrix. If A is a square matrix, then the determinant is M_ij.

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To find:

The all minors and cofactors of the given matrix A=[1230−15214].

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Chapter 8 Solutions

The all minors and cofactors of the given matrix A = [ 1 2 3 0 − 1 5 2 1 4 ] .

Solution Summary: The author explains how to find the minors and cofactors of the given matrix. If A is a square matrix, then the determinant is M_ij.

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To find: The all minors and cofactors of the given matrix A=[1230−15214].

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Chapter 8 Solutions

To find:

The all minors and cofactors of the given matrix A=[1230−15214].