Question

find inverse of matrice by elementary transformation
class 12
math
pls urgent ​

Answer 1

$A = \left[\begin{array}{ccc}2&1\\1&1\\\end{array}\right]$

$A = IA$, where I is the identity matrix of order 2

$\left[\begin{array}{ccc}2&1\\1&1\\\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right] A$

$R_1\rightarrow R_1-R_2$

$\left[\begin{array}{ccc}1&0\\1&1\\\end{array}\right] = \left[\begin{array}{ccc}1&-1\\0&1\\\end{array}\right] A$

$R_2\rightarrow R_2-R_1$

$\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right] = \left[\begin{array}{ccc}1&-1\\-1&2\\\end{array}\right] A$

This is of the form

$I = A^{-1}A$

Hence,

$A^{-1} =\left[\begin{array}{ccc}1&-1\\-1&2\\\end{array}\right]$

HOPE THIS HELPS!!