Question

If $A=\left[\begin{array}{ccc}\sqrt{3}& 1& -1\\ 2& 3& 0\end{array}\right]$ and $B=\left[\begin{array}{ccc}2& \sqrt{5}& 1\\ -2& 3& \frac{1}{2}\end{array}\right]$, then the value of $A+B$ is

• A. $\left[\begin{array}{ccc}2+\sqrt{3}& -1+\sqrt{5}& 0\\ 0& 3& \frac{1}{2}\end{array}\right]$
• B. $\left[\begin{array}{ccc}-1+\sqrt{3}& 1+\sqrt{5}& 0\\ 0& 6& \frac{1}{6}\end{array}\right]$
• C. $\left[\begin{array}{ccc}2+\sqrt{3}& 1+\sqrt{5}& 0\\ 0& 6& \frac{1}{2}\end{array}\right]$
• D. $\left[\begin{array}{ccc}2+\sqrt{3}& 1-\sqrt{5}& 0\\ 0& 6& \frac{1}{2}\end{array}\right]$

Answer 1

The correct option is C $\left[\begin{array}{ccc}2+\sqrt{3}& 1+\sqrt{5}& 0\\ 0& 6& \frac{1}{2}\end{array}\right]$

Since $A,B$ are of the same order $2\times 3$. Therefore, addition of $A$ and $B$ is defined and is given by:
$A+B=\left[\begin{array}{ccc}2+\sqrt{3}& 1+\sqrt{5}& 1-1\\ 2-2& 3+3& 0+\frac{1}{2}\end{array}\right]=\left[\begin{array}{ccc}2+\sqrt{3}& 1+\sqrt{5}& 0\\ 0& 6& \frac{1}{2}\end{array}\right]$