Find the adjoint of matrix A = $\left[\begin{array}{lll}{2} & {5} & {3} \\ {3} & {1} & {2} \\ {1} & {2} & {1}\end{array}\right]$

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written 5.6 years ago by

teamques10 ★ 69k

Solution:

let A =

$\begin{bmatrix} 2 & 5 & 3\ 3 & 1 & 2\ 1 & 2 & 1 \end{bmatrix}$

$Matrix of minors = \quad \begin{bmatrix} \quad \begin{vmatrix} 1 & 2 \\ 2 & 1 \end{vmatrix} & \quad \begin{vmatrix} 3 & 2 \\ 1 & 1 \end{vmatrix} & \quad \begin{vmatrix} 3 & 1 \\ 1 & 2 \end{vmatrix} \\ \quad \begin{vmatrix} 5 & 3 \\ 2 & 1 \end{vmatrix} & \quad \begin{vmatrix} 2 & 3 \\ 1 & 1 \end{vmatrix} & \quad \begin{vmatrix} 2 & 5 \\ 1 & 2 \end{vmatrix}\\ \quad \begin{vmatrix} 5 & 3 \\ 1 & 2 \end{vmatrix} & \quad \begin{vmatrix} 2 & 3 \\ 3 & 2 \end{vmatrix} & \quad \begin{vmatrix} 2 & 5 \\ 3 & 1 \end{vmatrix} \\ \end{bmatrix}$

$\begin{bmatrix} -3 & 1 & 5 \ -1 & -1 & -1\ 7 & 5 & -13 \end{bmatrix}$

$Adj A = \quad \begin{bmatrix} -3 & 1 & 7 \\ 1 & -1 & 5\\ 5 & 1 & -13 \end{bmatrix}$

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