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The rank of the matrix $\begin{bmatrix} 1 & -1 & 2 \\2 & -2 & 4 \\4 & -4 & 8 \end{bmatrix}$ is

\[\begin{array}{1 1}(1)1 & (2)2 \\ (3)3 & (4)4\end{array}\]

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$A=\begin{bmatrix} 1 & -1 & 2 \\2 & -2 & 4 \\4 & -4 & 8 \end{bmatrix}$
$\quad = \begin{bmatrix} 1 & -1 & 2 \\0 & 0 & 0 \\0 & 0 & 0 \end{bmatrix}$
$R_2 \to R_2 - 2R_1$
$R_3 \to R_3 - 4R_1$
No. of o zero row =1
p(A) =1
Hence A is the correct answer.
answered May 2, 2014 by meena.p
 

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