If A - begin bmatrix -18283115 - 7 - 9 -2 - 1 - 1lend bmatrix and B - begin bmatrix -4 - 1 -5 182280 1 - 3 - 1 lend bmatrix - then verify that ii A - B - A - B -

Here, A B =[ 1 amp; 2 amp; 3; 5 amp; 7 amp; 9; 2 amp; 1 amp; 1; ] [ 4 amp; 1 amp; 5; 1 amp; 2 amp; 0; 1 amp; 3 amp ...

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Byju's Answer

Standard XII

Mathematics

Addition and Subtraction of a Matrix

If A = begin ...

Question

If $A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 3 5 & 7 & 9 - 2 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ and $B = ⎡ ⎢ ⎣ \begin{matrix} - 4 & 1 & - 5 1 & 2 & 0 1 & 3 & 1 \end{matrix} ⎤ ⎥ ⎦$ , then verify that
(ii)(A-B)'=A'-B'

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Solution

Here, $A - B = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 3 5 & 7 & 9 - 2 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦ - ⎡ ⎢ ⎣ \begin{matrix} - 4 & 1 & - 5 1 & 2 & 0 1 & 3 & 1 \end{matrix} ⎤ ⎥ ⎦$

$= ⎡ ⎢ ⎣ \begin{matrix} - 1 + 4 & 2 - 1 & 3 + 5 5 - 1 & 7 - 2 & 9 - 0 - 2 - 1 & 1 - 3 & 1 - 1 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 3 & 1 & 8 4 & 5 & 9 - 3 & - 2 & 0 \end{matrix} ⎤ ⎥ ⎦$
$\Rightarrow (A - B)^{'} = ⎡ ⎢ ⎣ \begin{matrix} 3 & 4 & - 3 1 & 5 & - 2 8 & 9 & 0 \end{matrix} ⎤ ⎥ ⎦ . . . . . (i)$
Also, $A^{'} - B^{'} = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 5 & - 2 2 & 7 & 1 3 & 9 & 1 \end{matrix} ⎤ ⎥ ⎦ - ⎡ ⎢ ⎣ \begin{matrix} - 4 & 1 & 1 1 & 2 & 3 - 5 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 + 4 & 5 - 1 & - 2 - 1 2 - 1 & 7 - 2 & 1 - 3 3 - (- 5) & 9 - 0 & 1 - 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} 3 & 4 & - 3 1 & 5 & - 2 8 & 9 & 0 \end{matrix} ⎤ ⎥ ⎦ . . . . . . . . . . . . . (i i)$
From Eqs.(i)and (ii), it is verified that (A-B)'=A'-B'.

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Similar questions

If $A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 3 5 & 7 & 9 - 2 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ and $B = ⎡ ⎢ ⎣ \begin{matrix} - 4 & 1 & - 5 1 & 2 & 0 1 & 3 & 1 \end{matrix} ⎤ ⎥ ⎦$ , then verify that
(i)(A+B)'=A'+B'

(ii)(A-B)'=A'-B'

Q. If

A = [\begin{matrix} 3 & 2 7 & 5 \end{matrix}]

and

B = [\begin{matrix} 6 & 7 8 & 9 \end{matrix}]

, verify that

(A B)^{- 1} = B^{- 1} A^{- 1}

Q. Let

A = [\begin{matrix} 3 & 7 2 & 5 \end{matrix}]

and

B = [\begin{matrix} 6 & 8 7 & 9 \end{matrix}]

. Verify that

{(A B)}^{- 1}

B^{- 1}

A^{- 1}

Q. If

A = [\begin{matrix} 3 & 2 - 1 & 4 \end{matrix}]; B = [\begin{matrix} - 2 & 5 6 & 7 \end{matrix}]

and

C = [\begin{matrix} 1 & 1 - 5 & 3 \end{matrix}]

verify that

A (B + C) = A B + A C .

Q. If

A = [\begin{matrix} 2 & 3 1 & - 4 \end{matrix}]

and

B = [\begin{matrix} 1 & - 2 - 1 & 3 \end{matrix}]

, then verify that

{(A B)}^{- 1} = B^{- 1} A^{- 1}

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If A=⎡⎢⎣−123579−211⎤⎥⎦ and B=⎡⎢⎣−41−5120131⎤⎥⎦, then verify that (ii)(A-B)'=A'-B'

If $A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 3 5 & 7 & 9 - 2 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ and $B = ⎡ ⎢ ⎣ \begin{matrix} - 4 & 1 & - 5 1 & 2 & 0 1 & 3 & 1 \end{matrix} ⎤ ⎥ ⎦$ , then verify that
(ii)(A-B)'=A'-B'