Question:
If matrix $A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]$, write $A A^{\top}$.
Solution:
Given: $A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]$
$A^{T}=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$
$A A^{T}=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$
$\Rightarrow A A^{T}=1+4+9$
$\Rightarrow A A^{T}=14$
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