If A=[1421],B=[−3240] and C=[1002], then A2+BC=

A2=A.A=[1421][1421]=[1+84+42+28+1]=[9849]BC=[−3240][1002]=[−3+00+44+00+0]=[−3440]A2+BC=[9849]+[−3440]=[9−38+44+49+0]=[61289]

If A=[1421],B=[−3240] and C=[1002], then A2+BC=

A2=A.A=[1421][1421]=[1+84+42+28+1]=[9849]BC=[−3240][1002]=[−3+00+44+00+0]=[−3440]A2+BC=[9849]+[−3440]=[9−38+44+49+0]=[61289]

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If $A = [\begin{matrix} 1 & 4 \\ 2 & 1 \end{matrix}], B = [\begin{matrix} - 3 & 2 \\ 4 & 0 \end{matrix}] a n d C = [\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix}]$ , then $A^{2} + B C =$

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$[\begin{matrix} 9 & 8 \\ 4 & 9 \end{matrix}]$

$[\begin{matrix} 6 & 12 \\ 8 & 9 \end{matrix}]$

$[\begin{matrix} 12 & 12 \\ 8 & 9 \end{matrix}]$

$[\begin{matrix} - 3 & 4 \\ 4 & 0 \end{matrix}]$

answer is C.

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Detailed Solution

$A^{2} = A . A = [\begin{matrix} 1 & 4 \\ 2 & 1 \end{matrix}] [\begin{matrix} 1 & 4 \\ 2 & 1 \end{matrix}] = [\begin{matrix} 1 + 8 & 4 + 4 \\ 2 + 2 & 8 + 1 \end{matrix}] = [\begin{matrix} 9 & 8 \\ 4 & 9 \end{matrix}]$

$B C = [\begin{matrix} - 3 & 2 \\ 4 & 0 \end{matrix}] [\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix}] = [\begin{matrix} - 3 + 0 & 0 + 4 \\ 4 + 0 & 0 + 0 \end{matrix}] = [\begin{matrix} - 3 & 4 \\ 4 & 0 \end{matrix}]$

$A^{2} + B C = [\begin{matrix} 9 & 8 \\ 4 & 9 \end{matrix}] + [\begin{matrix} - 3 & 4 \\ 4 & 0 \end{matrix}] = [\begin{matrix} 9 - 3 & 8 + 4 \\ 4 + 4 & 9 + 0 \end{matrix}] = [\begin{matrix} 6 & 12 \\ 8 & 9 \end{matrix}]$