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# The rank of the diagonal matrix $\begin{bmatrix} -1 & & \\ & -2 & \\ & & 0\\& & &-4\\ & & & &0 \end{bmatrix}$

$\begin{array}{1 1} (1) 0& (2)2 \\(3) 3&(4) 5\end{array}$

$A=\begin{bmatrix} -1 & & \\ & 2 & \\ & & 0\\& & &-4\\ & & & &0 \end{bmatrix}$
$A=\begin{bmatrix} -1 & 0 & 0 & 0 & 0 \\ 0 & -2 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 &-4 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix}$
The No. of non zero rows in $A =3$
$\therefore P(A)=3$
Hence 3 is the correct answer
edited May 2, 2014 by meena.p