Question

If $A=\left[\begin{array}{ccc}2& 3& 4\\ 0& -1& -2\end{array}\right],B=\left[\begin{array}{ccc}0& -2& -7\\ 3& -1& 5\end{array}\right]\text{and}C=\left[\begin{array}{ccc}1& -1& 0\\ 2& 0& -6\end{array}\right]$
Find a matrix X sucn that C+X=A+B

• A. $\left[\begin{array}{ccc}1& 2& 3\\ 1& 2& 9\end{array}\right]$
• B. $\left[\begin{array}{ccc}1& 2& -3\\ 1& -2& 9\end{array}\right]$
• C. $\left[\begin{array}{ccc}1& -2& -3\\ 3& -2& 7\end{array}\right]$
• D. $\left[\begin{array}{ccc}1& 2& 4\\ 1& 0& 9\end{array}\right]$

Answer 1

The correct option is B

$\left[\begin{array}{ccc}1& 2& -3\\ 1& -2& 9\end{array}\right]$

$C+X=A+B\therefore X=A+B-C$
If $A=\left[\begin{array}{ccc}2& 3& 4\\ 0& -1& -2\end{array}\right],B=\left[\begin{array}{ccc}0& -2& -7\\ 3& -1& 5\end{array}\right]\text{and}C=\left[\begin{array}{ccc}1& -1& 0\\ 2& 0& -6\end{array}\right]$

$A+B=\left[\begin{array}{ccc}2+0& 3-2& 4-7\\ 0+3& -1-1& -2+5\end{array}\right]=\left[\begin{array}{ccc}2& 1& -3\\ 3& -2& 3\end{array}\right]$

$A+B-C=\left[\begin{array}{ccc}2-1& 1+1& -3-0\\ 3-2& -2-0& 3+6\end{array}\right]=\left[\begin{array}{ccc}1& 2& -3\\ 1& -2& 9\end{array}\right]$