Question

Find the value of $x,y,z$ and $w$ which satisfy the matrix equation
$\left[\begin{array}{cc}x+3& 2y+x\\ z-1& 4w-8\end{array}\right]=\left[\begin{array}{cc}-x-1& 0\\ 3& 2w\end{array}\right]$
Then fill in the value of $x+2y+3z+4w$

Answer 1

Given : $\left[\begin{array}{cc}x+3& 2y+x\\ z-1& 4w-8\end{array}\right]=\left[\begin{array}{cc}-x-1& 0\\ 3& 2w\end{array}\right]$

As the given matrices are equal, so their corresponding elements are equal
i.e. $x+3=-x-1\Rightarrow 2x=-4\therefore x=-2$
$2y+x=0\Rightarrow 2y-2=0\therefore y=1$
$z-1=3\Rightarrow z=4$
$4w-8=2w\Rightarrow 2w=8\therefore w=4$
$\Rightarrow x+2y+3z+4w=28$