Find the adjoint of the following matrix. Find the cofactor of matrix A in quest

Question

Find the adjoint of the following matrix. Find the cofactor of matrix A in question 1 above If matrix A is given as use the formula A^1 = adj A/|A| to find its inverse. If matrix A is given as use the formula A^1 = adj A/|A| to find its inverse. For matrix A in question 3 above, use Gauss-Jordan elimination to transform [A |1] into [I | A^-1] Using the matrix show that AA^1 = A^_1A = I Identify the diagonal and off-diagonal elements of B. Find the transpose B'. Show that the transpose of B' equals B. That is, (B1)' = B.

Explanation / Answer

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To calculate adjoint of matrix we have to follow the procedure a) Calculate Minor for each element of the matrix. b) Form Cofactor matrix from the minors calculated. c) Form Adjoint from cofactor matrix.

1. minor =[ 24 -5 -4 ]

[12 3 -2 ]

[ -2 5 4 ]

2. cofactor (-1) Minor ^(row+column)

[ 24 5 -4 ]

[12 -3 -2 ]

[ -2 -5 4 ]

3. hence adjoint is :

[ 24 5 -4 ]

[12 -3 -2 ]

[ -2 -5 4 ]

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