Question

Let A = $\begin{bmatrix} 2 & 3 \

• 1 & 5 \end{bmatrix}$if A^–1 = xA + yI₂ then x and y are

respectively –

• A. $\frac{1}{13}$, $\frac{- 7}{13}$
• B. $\frac{7}{13}$,$\frac{- 1}{13}$
• C. $\frac{- 1}{13}$,$\frac{7}{13}$
• D. $\frac{- 7}{13}$,$\frac{1}{13}$

Answer 1

Answer: (C)

$\frac{- 1}{13}$,$\frac{7}{13}$

Answer 2

A^–1 = $\frac { 1 } { 13 }$ $\begin{bmatrix} 5 & - 3 \\ 1 & 2 \end{bmatrix}$= x$\begin{bmatrix} 2 & 3 \

• 1 & 5 \end{bmatrix}$+ y$\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$

Ž $\frac{5}{13}$ = 2x + y, $\frac{- 3}{13}$ =3x

Ž $\frac{1}{13}$ = –x, $\frac{2}{13}$ = 5x + y

x = $\frac{- 1}{13}$, y =$\frac{7}{13}$.