If A - bmatrix 3 - 411-1 - 2 0 - 1lendbmatrix and B - beginbmatrix -1 - 2 - 1111 - 2 - 3 lend bmatrix - then verify that ii A - B - A - B -

∴ A=(A')'=[ 3 amp; 4; 1 amp; 2; 0 amp; 1 ]=[ 3 amp; 1 amp; 0; 4 amp; 2 amp; 1; ] Here, RHS=A' B'=[ 3 amp;4; 1 ...

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Byju's Answer

Standard XII

Mathematics

Inverse of a Matrix

If A '=. bmat...

Question

If $A^{'} = ⎡ ⎢ ⎣ \begin{matrix} 3 & 4 - 1 & 2 0 & 1 \end{matrix} ⎤ ⎥ ⎦$ and $B = [\begin{matrix} - 1 & 2 & 1 1 & 2 & 3 \end{matrix}]$ , then verify that
(ii)(A-B)'=A'-B'

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Solution

$∴ A = (A^{'})^{'} = ⎡ ⎢ ⎣ \begin{matrix} 3 & 4 - 1 & 2 0 & 1 \end{matrix} ⎤ ⎥ ⎦ = [\begin{matrix} 3 & - 1 & 0 4 & 2 & 1 \end{matrix}]$
Here, $R H S = A^{'} - B^{'} = ⎡ ⎢ ⎣ \begin{matrix} 3 & 4 - 1 & 2 0 & 1 \end{matrix} ⎤ ⎥ ⎦ - ⎡ ⎢ ⎣ \begin{matrix} - 1 & 1 2 & 2 1 & 3 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 3 + 1 & 4 - 1 - 1 - 2 & 2 - 2 0 - 1 & 1 - 3 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 4 & 3 - 3 & 0 - 1 & - 2 \end{matrix} ⎤ ⎥ ⎦$
Also $(A - B)^{'} = {([\begin{matrix} 3 & - 1 & 0 4 & 2 & 1 \end{matrix}] - [\begin{matrix} - 1 & 2 & 1 1 & 2 & 3 \end{matrix}])}^{'} (∵ A = (A^{'})^{'}) = [\begin{matrix} 3 + 1 & - 1 - 2 & 0 - 1 4 - 1 & 2 - 2 & 1 - 3 \end{matrix}] = {[\begin{matrix} 4 & - 3 & - 1 3 & 0 & - 2 \end{matrix}]}^{'} = ⎡ ⎢ ⎣ \begin{matrix} 4 & 3 - 3 & 0 - 1 & - 2 \end{matrix} ⎤ ⎥ ⎦$
So, verified that (A-B)'=A'-B'

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