Find the inverse of the matrix - - 1 0 0- 3 3 0- 5 2 1 -

A=[ 1 amp; 0 amp; 0; 3 amp; 3 amp; 0; 5 amp; 2 amp; 1 ], | A | =1(3)=3 AdjA=[ 3 amp; 0 amp; 0; 3 amp; 1 amp; 0; ...

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Standard XII

Mathematics

Finding Inverse Using Elementary Transformations

Find the inve...

Question

Find the inverse of the matrix
$⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 3 & 3 & 0 5 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦$

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Solution

$A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 3 & 3 & 0 5 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦, | A | = 1 (3) = 3 A d j A = ⎡ ⎢ ⎣ \begin{matrix} 3 & 0 & 0 - 3 & 1 & 0 9 & - 2 & 3 \end{matrix} ⎤ ⎥ ⎦ ∴ A^{- 1} = \frac{A d j A}{| A |} = \frac{1}{3} ⎡ ⎢ ⎣ \begin{matrix} 3 & 0 & 0 - 3 & 1 & 0 9 & - 2 & 3 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 - 1 & \frac{1}{3} & 0 3 & \frac{- 2}{3} & 1 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$

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Find the inverse of the matrix⎡⎢⎣100330521⎤⎥⎦

A=⎡⎢⎣100330521⎤⎥⎦,|A|=1(3)=3AdjA=⎡⎢⎣300−3109−23⎤⎥⎦∴A−1=AdjA|A|=13⎡⎢⎣300−3109−23⎤⎥⎦=⎡⎢ ⎢ ⎢ ⎢ ⎢⎣100−11303−231⎤⎥ ⎥ ⎥ ⎥ ⎥⎦

Find the inverse of the matrix
$⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 3 & 3 & 0 5 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦$