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Inverse of a Matrix

If A=[ x y ],...

Question

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

A

(a x + h y + b x y)

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B

(a x^{2} + 2 h x y + b y^{2})

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C

(a x^{2} - 2 h x y + b y^{2})

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D

(b x^{2} - 2 h x y + a y^{2})

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Solution

The correct option is B $(a x^{2} + 2 h x y + b y^{2})$
Given: $A = [\begin{matrix} x & y \end{matrix}], B = [\begin{matrix} a & h h & b \end{matrix}], C = [\begin{matrix} x y \end{matrix}]$
$A B C = [\begin{matrix} x & y \end{matrix}] [\begin{matrix} a & h h & b \end{matrix}] [\begin{matrix} x y \end{matrix}]$
$= [\begin{matrix} a x + h y & x h + b y \end{matrix}] [\begin{matrix} x y \end{matrix}] = a x^{2} + h x y + x y h + b y^{2}$
= $a x^{2} + 2 h x y + b y^{2}$

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Inverse of a Matrix

Standard XII Mathematics

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