Question

If $A=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right],$ then AA^T = __________.

Answer 1

The given matrix is $A=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$.
$\therefore A{A}^T$

$=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]{\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]}^T$

$=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$

$=\left[\begin{array}{ccc}1\times 1& 1\times 2& 1\times 3\\ 2\times 1& 2\times 2& 2\times 3\\ 3\times 1& 3\times 2& 3\times 3\end{array}\right]$

$=\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& 6\\ 3& 6& 9\end{array}\right]$


If $A=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right],$ then AA^T = $\underline{\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& 6\\ 3& 6& 9\end{array}\right]}$.