Question

Let $A=\left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 0\end{array}\right],B=\left[\begin{array}{ccc}0& 1& -1\\ 1& 2& 3\end{array}\right],\text{and}C=\left[\begin{array}{ccc}-1& 2& 3\\ 0& 0& 1\end{array}\right]$

Find each of the following :

(vii) $A-\left(B-C\right)$

Answer 1

Calculation of the matrix $A-\left(B-C\right)$.

The subtraction of matrices is defined as the subtraction of corresponding elements of two or more matrices.

$\begin{array}{rcl}A-\left(B-C\right)& =& \left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 0\end{array}\right]-\left(\left[\begin{array}{ccc}0& 1& -1\\ 1& 2& 3\end{array}\right]-\left[\begin{array}{ccc}-1& 2& 3\\ 0& 0& 1\end{array}\right]\right)\\ & =& \left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 0\end{array}\right]-\left[\begin{array}{ccc}0-\left(-1\right)& 1-2& -1-3\\ 1-0& 2-0& 3-1\end{array}\right]\\ & =& \left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 0\end{array}\right]-\left[\begin{array}{ccc}0+1& -1& -4\\ 1& 2& 2\end{array}\right]\\ & =& \left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 0\end{array}\right]-\left[\begin{array}{ccc}1& -1& -4\\ 1& 2& 2\end{array}\right]\\ & =& \left[\begin{array}{ccc}1-1& -1-\left(-1\right)& 2-\left(-4\right)\\ 2-1& 1-2& 0-2\end{array}\right]\\ & =& \left[\begin{array}{ccc}0& -1+1& 2+4\\ 1& -1& -2\end{array}\right]\\ & =& \left[\begin{array}{ccc}0& 0& 6\\ 1& -1& -2\end{array}\right]\end{array}$

Final answer: The result is $\begin{array}{l}\left[\begin{array}{ccc}0& 0& 6\\ 1& -1& -2\end{array}\right]\end{array}$.