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Given $A=\left[\begin{array}{ccc}\sqrt{3} & 1 & -1 \\ 2 & 3 & 0\end{array}\right]$ and $B=\left[\begin{array}{ccc}2 & \sqrt{5} & 1 \\ -2 & 3 & \frac{1}{2}\end{array}\right],$ find $A+B$ $=$ ........
$ \left[ {\begin{array}{*{20}{c}}
{2 - \sqrt 3 }&{1 + \sqrt 5 }&0 \\
0&6&{\frac{1}{2}}
\end{array}} \right]$
$ \left[ {\begin{array}{*{20}{c}}
{2 + \sqrt 3 }&{1 + \sqrt 5 }&0 \\
0&6&{\frac{1}{2}}
\end{array}} \right]$
$ \left[ {\begin{array}{*{20}{c}}
{2 + \sqrt 3 }&{1 - \sqrt 5 }&0 \\
0&6&{\frac{1}{2}}
\end{array}} \right]$
$ \left[ {\begin{array}{*{20}{c}}
{2 + \sqrt 3 }&{1- \sqrt 5 }&0 \\
0&6&{\frac{-1}{2}}
\end{array}} \right]$
Solution
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 = $ $\left[ {\begin{array}{*{20}{l}}
{2 + \sqrt 3 }&{1 + \sqrt 5 }&{1 – 1} \\
{2 – 2}&{3 + 3}&{0 + \frac{1}{2}}
\end{array}} \right]$
$ = \left[ {\begin{array}{*{20}{c}}
{2 + \sqrt 3 }&{1 + \sqrt 5 }&0 \\
0&6&{\frac{1}{2}}
\end{array}} \right]$
