Question

Find a matrix X such that A-X=B, given

$A=\left(\begin{array}{ccc}3& 7& 2\\ -4& -3& 0\\ 5& 1& -2\end{array}\right)andB=\left(\begin{array}{ccc}8& -6& 1\\ 2& 0& -3\\ 3& 4& -1\end{array}\right)$

• A. $\left(\begin{array}{ccc}-5& 13& 1\\ 7& 3& 3\\ 2& 3& -1\end{array}\right)$
• B. $\left(\begin{array}{ccc}5& 1& 1\\ -7& 3& 3\\ 2& -3& 1\end{array}\right)$
• C. $\left(\begin{array}{ccc}5& 1& 1\\ 7& -3& 3\\ 2& -3& -1\end{array}\right)$
• D. $\left(\begin{array}{ccc}-5& 13& 1\\ -7& -3& 3\\ 2& -3& -1\end{array}\right)$

Answer 1

The correct option is D

$\left(\begin{array}{ccc}-5& 13& 1\\ -7& -3& 3\\ 2& -3& -1\end{array}\right)$

Given:
$A-X=B\Rightarrow X=A-B$

$A=\left(\begin{array}{ccc}3& 7& 2\\ -4& -3& 0\\ 5& 1& -2\end{array}\right)andB=\left(\begin{array}{ccc}8& -6& 1\\ 2& 0& -3\\ 3& 4& -1\end{array}\right)$

$A-B=\left(\begin{array}{ccc}3-8& 7+6& 2-1\\ -4-2& -3-0& 0+3\\ 5-3& 1-4& -2+1\end{array}\right)$

$=\left(\begin{array}{ccc}-5& 13& 1\\ -7& -3& 3\\ 2& -3& -1\end{array}\right)$