The rank of the Matrix 10201-21-14228 is

The rank of the Matrix 10201-21-14228 isR3→R3−R1R4→R4−2R110201-20-12024R3→R3+R2R4→R4+2R210201-2000008R3↔R410201-2008000Rank =3

The rank of the Matrix 10201-21-14228 is

The rank of the Matrix 10201-21-14228 isR3→R3−R1R4→R4−2R110201-20-12024R3→R3+R2R4→R4+2R210201-2000008R3↔R410201-2008000Rank =3

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The rank of the Matrix $[\begin{matrix} 1 & 0 & 2 \\ 0 & 1 & - 2 \\ 1 & - 1 & 4 \\ 2 & 2 & 8 \end{matrix}] \begin{matrix} \end{matrix}$ is

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answer is B.

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Detailed Solution

The rank of the Matrix $[\begin{matrix} 1 & 0 & 2 \\ 0 & 1 & - 2 \\ 1 & - 1 & 4 \\ 2 & 2 & 8 \end{matrix}] \begin{matrix} \end{matrix}$ is
$\begin{aligned} R_{3} \to R_{3} - R_{1} \\ R_{4} \to R_{4} - 2 R_{1} \end{aligned} [\begin{matrix} 1 & 0 & 2 \\ 0 & 1 & - 2 \\ 0 & - 1 & 2 \\ 0 & 2 & 4 \end{matrix}]$
$\begin{aligned} R_{3} \to R_{3} + R_{2} \\ R_{4} \to R_{4} + 2 R_{2} \end{aligned} [\begin{matrix} 1 & 0 & 2 \\ 0 & 1 & - 2 \\ 0 & 0 & 0 \\ 0 & 0 & 8 \end{matrix}]$
$R_{3} \leftrightarrow R_{4} [\begin{matrix} 1 & 0 & 2 \\ 0 & 1 & - 2 \\ 0 & 0 & 8 \\ 0 & 0 & 0 \end{matrix}]$
Rank =3