If A - - 3 x- 0 1 - and B - - 9 16- 0 -y - find- x- and- y -when- A2 - B

Now A^2 = A * A = gt; [ 3 amp;x; 0 amp; 1 ]*[ 3 amp;x; 0 amp; 1 ] = gt; [ 9 amp;3x+x; 0 amp; 1 ] = gt; [ ...

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Byju's Answer

Standard X

Mathematics

Multiplication of Matrices

If A = [ 3 x;...

Question

If $A = [\begin{matrix} 3 & x 0 & 1 \end{matrix}] a n d B = [\begin{matrix} 9 & 16 0 & - y \end{matrix}], f i n d x a n d y w h e n A^{2} = B$

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Solution

Now
$A^{2} = A * A => [\begin{matrix} 3 & x 0 & 1 \end{matrix}]$ * $[\begin{matrix} 3 & x 0 & 1 \end{matrix}]$

=> $[\begin{matrix} 9 & 3 x + x 0 & 1 \end{matrix}]$

=> $[\begin{matrix} 9 & 4 x 0 & 1 \end{matrix}] w e h a v e A^{2} = B$

two matrices are equal if each and every corresponding element is equal

=> $[\begin{matrix} 9 & 4 x 0 & 1 \end{matrix}]$ = $[\begin{matrix} 9 & 16 0 & - y \end{matrix}]$

=>4x = 16 and 1=-y

=> x = 4 and y = -1

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If A=[3x01]andB=[9160−y],find x and y when A2=B

Now A2=A∗A=>[3x01]*[3x01] => [93x+x01] => [94x01]we have A2=B two matrices are equal if each and every corresponding element is equal =>[94x01] =[9160−y] =>4x = 16 and 1=-y => x = 4 and y = -1

If $A = [\begin{matrix} 3 & x 0 & 1 \end{matrix}] a n d B = [\begin{matrix} 9 & 16 0 & - y \end{matrix}], f i n d x a n d y w h e n A^{2} = B$