Question

If $A=\text{diag}(2-59),B=\text{diag}(11-4)$ and $C=\text{diag}(-634)$, then find $A-2B$.

Answer 1

Here, $A=\left[\begin{array}{ccc}2& 0& 0\\ 0& -5& 0\\ 0& 0& 9\end{array}\right]$ and $B=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& -4\end{array}\right]$

$\Rightarrow$ $A-2B=$ $\left[\begin{array}{ccc}2& 0& 0\\ 0& -5& 0\\ 0& 0& 9\end{array}\right]-2\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& -4\end{array}\right]$

$=\left[\begin{array}{ccc}2& 0& 0\\ 0& -5& 0\\ 0& 0& 9\end{array}\right]-\left[\begin{array}{ccc}1\times 2& 0\times 2& 0\times 2\\ 0\times 2& 1\times 2& 0\times 2\\ 0\times 2& 0\times 2& -4\times 2\end{array}\right]$

$=\left[\begin{array}{ccc}2& 0& 0\\ 0& -5& 0\\ 0& 0& 9\end{array}\right]-\left[\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\\ 0& 0& -8\end{array}\right]$

$=\left[\begin{array}{ccc}2-2& 0-0& 0-0\\ 0-0& -5-2& 0-0\\ 0-0& 0-0& 9-(-8)\end{array}\right]$

$=\left[\begin{array}{ccc}0& 0& 0\\ 0& -7& 0\\ 0& 0& 17\end{array}\right]=diag(0-717)$