Find the inverse of the matrixA - - 1 2 3- 4 1 5- 3 6 9 -

A = [ 1 amp; 2 amp; 3; 4 amp; 1 amp; 5; 3 amp; 6 amp; 9 ] A^ 1 = adj A|A| = [ 21 amp; 21 amp; 21; 0 amp; 0 amp; 0; ...

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Standard XII

Mathematics

Adjoint of a Matrix

Find the inve...

Question

Find the inverse of the matrix
A = $⎡ ⎢ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 1 & 5 3 & 6 & 9 \end{matrix} ⎤ ⎥ ⎥ ⎦$

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Solution

$A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 1 & 5 3 & 6 & 9 \end{matrix} ⎤ ⎥ ⎦$
$A^{- 1} = \frac{a d j A}{| A |} = \frac{⎡ ⎢ ⎣ \begin{matrix} - 21 & - 21 & 21 0 & 0 & 0 7 & 7 & - 7 \end{matrix} ⎤ ⎥ ⎦}{| A |}$
$| A | = 0$
$∴$ Inverse doesn't exist

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Find the inverse of the matrixA = ⎡⎢ ⎢⎣123415369⎤⎥ ⎥⎦

A=⎡⎢⎣123415369⎤⎥⎦A−1=adjA|A|=⎡⎢⎣−21−212100077−7⎤⎥⎦|A||A|=0∴ Inverse doesn't exist

Find the inverse of the matrix
A = $⎡ ⎢ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 1 & 5 3 & 6 & 9 \end{matrix} ⎤ ⎥ ⎥ ⎦$

$A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 1 & 5 3 & 6 & 9 \end{matrix} ⎤ ⎥ ⎦$
$A^{- 1} = \frac{a d j A}{| A |} = \frac{⎡ ⎢ ⎣ \begin{matrix} - 21 & - 21 & 21 0 & 0 & 0 7 & 7 & - 7 \end{matrix} ⎤ ⎥ ⎦}{| A |}$
$| A | = 0$
$∴$ Inverse doesn't exist