If A=[x y], B=(a hh b),C=(xy) then ABC

AB=[ax+hyhx+by] ABC=[ax+hyhx+by][xy] =[ax2+2hxy+by2]

If A=[x y], B=(a hh b),C=(xy) then ABC

AB=[ax+hyhx+by] ABC=[ax+hyhx+by][xy] =[ax2+2hxy+by2]

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If $A = [x y], B = (\begin{matrix} a h \\ h b \end{matrix}), C = (\begin{matrix} x \\ y \end{matrix})$ then ABC

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$[a x + h y]$

$[a x^{2} + 2 h x y + b y^{2}]$

$[b x^{2} - 2 h x y + a y^{2}]$

$[a y + h x]$

answer is B.

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Detailed Solution

$A B = [\begin{matrix} a x + h y & h x + b y \end{matrix}]$

$A B C = [\begin{matrix} a x + h y & h x + b y \end{matrix}] [\begin{matrix} x \\ y \end{matrix}]$

$= [a x^{2} + 2 h x y + b y^{2}]$

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If $A = [x y], B = (\begin{matrix} a h \\ h b \end{matrix}), C = (\begin{matrix} x \\ y \end{matrix})$ then ABC