If A^ = [ cc 3 & 4 -1 & 2 0 & 1 ] and B= [ rrr -1 & 2 & 1 1 & 2 & 3 ] then verify (A + B)′ = A′ + B′

Given, A^ = [ cc 3 & 4 -1 & 2 0 & 1 ] and B= [ rrr -1 & 2 & 1 1 & 2 & 3 ] A= [ ccc 3 & -1 & 0 4 & 2 & 1 ] Now, A + B = [ ccc 3 & -1 & 0 4 & 2 & 1 ]+ [ ccc -1 & 2 & 1 1 & 2 & 3 ] A+B= [ ccc 3+(-1) & -1+2 & 0+1 4+1 & 2+2 & 1+3 ] A+B= [ lll 2 & 1 & 1 5 & 4 & 4 ] (A+B)' = [ ll 2 & 5 1 & 4 1 & 4 ] Therefore, (A+B)^ = [ ll 2 & 5 1 & 4 1 & 4 ]...(1) Now, A' + B' = [ cc 3 & 4 -1 & 2 0 & 1 ]+ [ cc -1 & 1 2 & 2 1 & 3 ] A^ +B^ = [ ll 2 & 5 1 & 4 1 & 4 ]...(2) From equation (1) & (2) we verify that (A+B)’ = A’+B’. Hence verified.

If A^ = [ cc 3 & 4 -1 & 2 0 & 1 ] and B= [ rrr -1 & 2 & 1 1 & 2 &…

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Question

If $A^{\prime}=\left[\begin{array}{cc} {3} & {4} \\ {-1} & {2} \\ {0} & {1} \end{array}\right] \text { and } B=\left[\begin{array}{rrr} {-1} & {2} & {1} \\ {1} & {2} & {3} \end{array}\right]$ then verify (A + B)′ = A′ + B′

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Answer

Given, $A^{\prime}=\left[\begin{array}{cc} {3} & {4} \\ {-1} & {2} \\ {0} & {1} \end{array}\right] \text { and } B=\left[\begin{array}{rrr} {-1} & {2} & {1} \\ {1} & {2} & {3} \end{array}\right]$
$\Rightarrow A=\left[\begin{array}{ccc} {3} & {-1} & {0} \\ {4} & {2} & {1} \end{array}\right]$
Now, A + B = $\left[\begin{array}{ccc} {3} & {-1} & {0} \\ {4} & {2} & {1} \end{array}\right]+\left[\begin{array}{ccc} {-1} & {2} & {1} \\ {1} & {2} & {3} \end{array}\right]$
$\Rightarrow A+B=\left[\begin{array}{ccc} {3+(-1)} & {-1+2} & {0+1} \\ {4+1} & {2+2} & {1+3} \end{array}\right]$
$\Rightarrow A+B=\left[\begin{array}{lll} {2} & {1} & {1} \\ {5} & {4} & {4} \end{array}\right]$
$\Rightarrow (A+B)' =\left[\begin{array}{ll} {2} & {5} \\ {1} & {4} \\ {1} & {4} \end{array}\right]$
Therefore, $(A+B)^\prime$ = $\left[\begin{array}{ll} {2} & {5} \\ {1} & {4} \\ {1} & {4} \end{array}\right]$...(1)
Now, A' + B' = $\left[\begin{array}{cc} {3} & {4} \\ {-1} & {2} \\ {0} & {1} \end{array}\right]+\left[\begin{array}{cc} {-1} & {1} \\ {2} & {2} \\ {1} & {3} \end{array}\right]$
$\Rightarrow A^{\prime}+B^{\prime}=\left[\begin{array}{ll} {2} & {5} \\ {1} & {4} \\ {1} & {4} \end{array}\right]$...(2)
From equation (1) & (2) we verify that
(A+B)’ = A’+B’. Hence verified.

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