Question
If $\text{A}=\begin{bmatrix} 1 & -3 \\ 2 & 0 \end{bmatrix},$ write adj A.
✓
Answer
$|\text{A}|=\begin{bmatrix} 1 & -3 \\ 2 & 0 \end{bmatrix}=6\neq0$
A is a non-singular matrix. Therefore, it is invertible.
Let Cij be a cofactor of aij in A.
The cofactors of element A are given by
C11 = 0
C12 = -2
C21 = 3
C22 = 1
$\therefore\ \text{adj A}=\text{A}=\begin{bmatrix} 0 & -2 \\ 3 & 1 \end{bmatrix}^\text{T}=\begin{bmatrix} 0 & 3 \\ -2 & 1 \end{bmatrix}$
A is a non-singular matrix. Therefore, it is invertible.
Let Cij be a cofactor of aij in A.
The cofactors of element A are given by
C11 = 0
C12 = -2
C21 = 3
C22 = 1
$\therefore\ \text{adj A}=\text{A}=\begin{bmatrix} 0 & -2 \\ 3 & 1 \end{bmatrix}^\text{T}=\begin{bmatrix} 0 & 3 \\ -2 & 1 \end{bmatrix}$
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