Question

If $A=\left[\begin{array}{cc}8& 0\\ 4& -2\\ 3& 6\end{array}\right]andB=\left[\begin{array}{cc}2& -2\\ 4& 2\\ -5& 1\end{array}\right]$, then find the matrix $X$, such that $2A+3X=5B$.

Answer 1

$A=\left[\begin{array}{cc}8& 0\\ 4& -2\\ 3& 6\end{array}\right]$ and

$B=\left[\begin{array}{cc}2& -2\\ 4& 2\\ -5& 1\end{array}\right]$

$2A=\left[\begin{array}{cc}16& 0\\ 8& -4\\ 6& 12\end{array}\right]$ and

$5B=\left[\begin{array}{cc}10& -10\\ 20& 10\\ -25& 5\end{array}\right]$

Now, $2A+3X=5B$

or, $2A-5B=3X$

or, $X=\frac{1}{3}(2A-5B)$

or, $X=\frac{1}{3}\left[\begin{array}{cc}16-10& 0+10\\ 8-20& -4-10\\ 6+25& 12-5\end{array}\right]$

or, $X=\frac{1}{3}\left[\begin{array}{cc}6& 10\\ -12& -14\\ 31& 7\end{array}\right]$