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 :

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

Answer 1

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

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

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

Final answer: The matrix is $\left[\begin{array}{ccc}2& -4& 0\\ 1& -1& -4\end{array}\right]$.