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# If A=$\begin{bmatrix} 2& 0& 1 \end{bmatrix}$ than the rank of $AA^{T}$is

$\begin{array}{1 1}(1) 1&(2) 2\\(3)3&(4) 0\end{array}$

A=$\begin{bmatrix} 2& 0& 1 \end{bmatrix}$
$A^T=\begin{bmatrix} 2 \\ 0 \\ 1 \end{bmatrix}$
$AA^T=\begin{bmatrix} 2& 0& 1 \end{bmatrix}\begin{bmatrix} 2 \\ 0 \\ 1 \end{bmatrix}$
$\qquad= \begin{bmatrix} 4+0+1=5 \end{bmatrix}$
The No. of non zero rows in $1$
$p(A)=1$
Hence 1 is the correct answer
edited May 2, 2014 by meena.p