Write A-1 for A= 2 & 5 1 & 3 - Vidyadip

Question

Write A^-1 for $\text{A}=\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}$

✓

Answer

$|\text{A}|=\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}=1\neq0$

Let C_ij be the cofactor of a_ij in A.

The cofactors of element A are given by

C₁₁ = 3

C₁₂ = -1

C₂₁ = -5

C₂₂ = 2

$\text{adj A}=\begin{bmatrix} 3 & -1 \\ -5 & 2 \end{bmatrix}^\text{T}=\begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}$

$|\text{A}|=6-5=1$

$\therefore\text{A}^{-1}=\frac{1}{|\text{A}|}\text{ adj A}=\begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}$

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