Find the adjoint of the following: (i) [(3,4),(6,2)] (ii) [(2,3,1),(3,4,1),(3,7,2)] (iii) (1/3)[(2,2,1),(-2,1,2),(1,-2,2)]

Question

Find the adjoint of the following:

(i) \(\begin{bmatrix} -3 &4 \\[0.3em] 6&2\\[0.3em] \end{bmatrix}\)

(ii) \(\begin{bmatrix} 2&3& 1 \\[0.3em] 3&4&1\\3 & 7 & 2\\[0.3em] \end{bmatrix}\)

(iii) (1/3)\(\begin{bmatrix} 2&2& 1 \\[0.3em] -2&1&2\\1& -2 & 2\\[0.3em] \end{bmatrix}\)

Answer 1

(i) \(\begin{bmatrix} -3 &4 \\[0.3em] 6&2\\[0.3em] \end{bmatrix}\)

If matrix

(ii) \(\begin{bmatrix} 2&3& 1 \\[0.3em] 3&4&1\\3 & 7 & 2\\[0.3em] \end{bmatrix}\)

Let A = \(\begin{bmatrix} 2&3& 1 \\[0.3em] 3&4&1\\3 & 7 & 2\\[0.3em] \end{bmatrix}\) adj A = (A_ij)T where (A_ij) = Co-factor matrix of A

Now

(iii) (1/3)\(\begin{bmatrix} 2&2& 1 \\[0.3em] -2&1&2\\1& -2 & 2\\[0.3em] \end{bmatrix}\)