Question

If $A=\left[\begin{array}{cc}1& -2\\ 3& 0\end{array}\right],B=\left[\begin{array}{cc}-1& 4\\ 2& 3\end{array}\right],C=\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$, then $5A-3B+2C=$

• A. $\left[\begin{array}{cc}8& 20\\ 7& 9\end{array}\right]$
• B. $\left[\begin{array}{cc}8& -20\\ 7& -9\end{array}\right]$
• C. $\left[\begin{array}{cc}-8& 20\\ -7& 9\end{array}\right]$
• D. $\left[\begin{array}{cc}8& 7\\ -20& -9\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{cc}8& -20\\ 7& -9\end{array}\right]$

Given, $A=\left[\begin{array}{cc}1& -2\\ 3& 0\end{array}\right],B=\left[\begin{array}{cc}-1& 4\\ 2& 3\end{array}\right],C=\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$
Consider $5A-3B+2C$
$=5\left[\begin{array}{cc}1& -2\\ 3& 0\end{array}\right]-3\left[\begin{array}{cc}-1& 4\\ 2& 3\end{array}\right]+2\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$
$=\left[\begin{array}{cc}5& -10\\ 15& 0\end{array}\right]+\left[\begin{array}{cc}3& -12\\ -6& -9\end{array}\right]+\left[\begin{array}{cc}0& 2\\ -2& 0\end{array}\right]$
$=\left[\begin{array}{cc}5+3+0& -10-12+2\\ 15-6-2& 0-9-0\end{array}\right]$
$=\left[\begin{array}{cc}8& -20\\ 7& -9\end{array}\right]$