Question

Find the values of a and b, if A= B, where $A=\left[\begin{array}{cc}a+4& 3b\\ 8& -6\end{array}\right]$ and $B=\left[\begin{array}{cc}2a+2& b^2+2\\ 8& b^2-5b\end{array}\right]$.

Answer 1

$A=B$

$\left[\begin{array}{cc}a+4& 3b\\ 8& -6\end{array}\right]=\left[\begin{array}{cc}2a+2& b^2+2\\ 8& b^2-5b\end{array}\right]$

On equating the corresponding elements, we get,

$a+4=2a+2$ .......(1)

$3b=b^2+2$ .......(2)

$-6=b^2-5b$ ........(3)

From equation 1, we get,

$a=2$

And, from equation 2 and 3, we get,

$b=2$