Question

If $A=diag\left[35\right]andB=diag[2-3]$, find A + 2B :

• A. $\left[\begin{array}{cc}7& 0\\ 0& -1\end{array}\right]$
• B. $\left[\begin{array}{cc}7& 0\\ 0& -2\end{array}\right]$
• C. $\left[\begin{array}{cc}6& 0\\ 0& -1\end{array}\right]$
• D. $\left[\begin{array}{cc}7& 1\\ 0& -1\end{array}\right]$

Answer 1

The correct option is A

$\left[\begin{array}{cc}7& 0\\ 0& -1\end{array}\right]$

Given $A=\left[\begin{array}{cc}3& 0\\ 0& 5\end{array}\right]andB=\left[\begin{array}{cc}2& 0\\ 0& -3\end{array}\right]$
$A+2B=\left[\begin{array}{cc}3+2\times 2& 0+2\times 0\\ 0+2\times 0& 5+2\times (-3)\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 0& -1\end{array}\right]$