Rank of the matrix given below is - 3 2 -9- -6 -4 18- 12 8 -36 -

[ 3 amp;2 nbsp; amp; 9; 6 nbsp; nbsp; amp; 4 nbsp; amp;18; 12 nbsp; nbsp; amp;8 nbsp; amp; 36 nbsp; ] [ 3 amp;2 ...

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Standard XII

Mathematics

Rank of a Matrix

Rank of the m...

Question

Rank of the matrix given below is :

$⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & - 9 - 6 & - 4 & 18 12 & 8 & - 36 \end{matrix} ⎤ ⎥ ⎦$

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\sqrt{2}

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Solution

The correct option is A 1
$⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & - 9 - 6 & - 4 & 18 12 & 8 & - 36 \end{matrix} ⎤ ⎥ ⎦$ $R_{2} \to R_{2} + 2 R_{1} - ------- \to R_{3} \to R_{3} - 4 R_{1}$ $⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & - 9 0 & 0 & 0 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦$

Rank of Matrix =1

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\begin{matrix} 4 & 6 & (25) 3 & 9 & (36) 8 & 6 & (. . . .) \end{matrix}

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. The rank of the matrix is _____ .

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Rank of the matrix given below is : ⎡⎢⎣32−9−6−418128−36⎤⎥⎦

The correct option is A 1⎡⎢⎣32−9−6−418128−36⎤⎥⎦ R2→R2+2R1−−−−−−−−→R3→R3−4R1 ⎡⎢⎣32−9000000⎤⎥⎦ Rank of Matrix =1

Rank of the matrix given below is :

$⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & - 9 - 6 & - 4 & 18 12 & 8 & - 36 \end{matrix} ⎤ ⎥ ⎦$

The correct option is A 1
$⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & - 9 - 6 & - 4 & 18 12 & 8 & - 36 \end{matrix} ⎤ ⎥ ⎦$ $R_{2} \to R_{2} + 2 R_{1} - ------- \to R_{3} \to R_{3} - 4 R_{1}$ $⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & - 9 0 & 0 & 0 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦$

Rank of Matrix =1