Question

if A=[x,y],B=[a h/h b],c=[x/y],
. then ABC-​

Answer 1

Answer:

$ABC=\left[\begin{array}{cc}ax^2+2hxy+by^2\end{array}\right]$

Step-by-step explanation:

Concept used:

The product of two matrices is defined if the number of columns of first matrix is equal to number of rows of second matrix

$A=\left[\begin{array}{cc}x&y\end{array}\right]$

$B=\left[\begin{array}{cc}a&h\\h&b\end{array}\right]$

$C=\left[\begin{array}{cc}x\\y\end{array}\right]$

Now,

$ABC=\left[\begin{array}{cc}x&y\end{array}\right].\left[\begin{array}{cc}a&h\\h&b\end{array}\right].\left[\begin{array}{cc}x\\y\end{array}\right]$

By matrix multiplication, we get

$ABC=\left[\begin{array}{cc}ax+hy&hx+by\end{array}\right].\left[\begin{array}{cc}x\\y\end{array}\right]$

$ABC=\left[\begin{array}{cc}(ax+hy)x+(hx+by)y\end{array}\right]$

$ABC=\left[\begin{array}{cc}ax^2+hxy+hxy+by^2\end{array}\right]$

$ABC=\left[\begin{array}{cc}ax^2+2hxy+by^2\end{array}\right]$

Answer 2

Answer:

ANSWER IS [ax² + 2xhy +by²]