If a matrix A= [ lll 1 & 2 & 3 ], then the matrix A A^ (where A^ … - Vidyadip

MCQ

If a matrix $A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right],$ then the matrix $A A^{\prime}\ ($where $A^{\prime}$ is the transpose of $A )$ is

A
$14$
B
$\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3\end{array}\right]$
C
$\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2\end{array}\right]$
✓
$[14]$

✓

Answer

Correct option: D.

$[14]$

$A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]$
$A^{\prime}=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$
So $, A A^{\prime}=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$
$=[1+4+9]=[14]$

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