Question

find intverse of matrix A​

Answer 1

Inverse of matrix A is $\left[\begin{array}{ccc}0.0161&0.1129\\0.1290&- 0.0367\\\end{array}\right]$

Given

To find inverse of matrix A

A = $\left[\begin{array}{ccc}6&7\\8&- 1\\\end{array}\right]$     $A^{-1\\}$  = ?

Formula :            

             $A^{-1\\}$ = $\frac{1}{ad - cb} . \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]$    -----> ( 1 )

             $A^{-1\\}$ =  $\frac{1}{ad - cb} . \left[\begin{array}{ccc}d&- b\\- c&a\\\end{array}\right]$  -----> ( 2 )

             $A^{-1\\}$ = $\left[\begin{array}{ccc}\frac{d}{ad - cb} &\frac{- b}{ad - cb}\\\frac{- c}{ad - cb} &\frac{a}{ad - cb}\\\end{array}\right]$  -----> ( 3 )

Here, a = 6   ;   b = 7   ;   c = 8   ;   d = - 1

Applying in above formula,

              $A^{-1\\}$ = $\frac{1}{( ( 6 ) . ( - 1 ) ) - ( ( 8 ) . ( 7 ) )}$  $\left[\begin{array}{ccc}6&7\\8&- 1\\\end{array}\right]$ -----> applying formula ( 1 )

                     =  $\frac{1}{- 6 - 56} \left[\begin{array}{ccc}- 1&- 7\\- 8&6\\\end{array}\right]$  -----> applying formula ( 2 )

                     = $\frac{1}{- 62} \left[\begin{array}{ccc}- 1&- 7\\- 8& 6\\\end{array}\right]$

                     = $\left[\begin{array}{ccc}\frac{- 1}{- 62} &\frac{- 7}{- 62} \\\frac{- 8}{- 62} &\frac{6}{-62} \\\end{array}\right]$  -----> applying formula ( 3 )

               $A^{-1}$ = $\left[\begin{array}{ccc}0.0161&0.1129\\0.1290&- 0.0367\\\end{array}\right]$

To learn more...

find intverse of matrix A​  = $\left[\begin{array}{ccc}6&7\\8&- 1\\\end{array}\right]$  

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