Question

If $A=\left[\begin{array}{cc}x& y\end{array}\right],B=\left[\begin{array}{cc}a& h\\ h& b\end{array}\right],C=\left[\begin{array}{c}x\\ y\end{array}\right]$, then $ABC=$

• A. $(ax+hy+bxy)$
• B. $(a{x}^2+2hxy+b{y}^2)$
• C. $(a{x}^2-2hxy+b{y}^2)$
• D. $(b{x}^2-2hxy+a{y}^2)$

Answer 1

The correct option is B $(a{x}^2+2hxy+b{y}^2)$

Given: $A=\left[\begin{array}{cc}x& y\end{array}\right],B=\left[\begin{array}{cc}a& h\\ h& b\end{array}\right],C=\left[\begin{array}{c}x\\ y\end{array}\right]$
$ABC=\left[\begin{array}{cc}x& y\end{array}\right]\left[\begin{array}{cc}a& h\\ h& b\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]$
$=\left[\begin{array}{cc}ax+hy& xh+by\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=a{x}^2+hxy+xyh+b{y}^2$
=$a{x}^2+2hxy+b{y}^2$