The Rank of - 1 0 -4- 2 -1 3 - is

The correct option is B 2 [ 1 amp; 0 amp; 4; 2 amp; 1 amp; 3 ] Converting into echelon form R _ 2 → R _ 2 2 R _ 1 [ 1 amp; ...

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Standard XII

Mathematics

Elementary Transformations

The Rank of ...

Question

The Rank of $[\begin{matrix} 1 & 0 & - 4 2 & - 1 & 3 \end{matrix}]$ is

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Solution

The correct option is B 2
$[\begin{matrix} 1 & 0 & - 4 2 & - 1 & 3 \end{matrix}]$
Converting into echelon form
$R_{2} \to R_{2} - 2 R_{1}$
$[\begin{matrix} 1 & 0 & - 4 0 & - 1 & 11 \end{matrix}]$
No. of non-zero rows $=$ rank of matrix
$= 2$

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The Rank of [10−42−13] is

The correct option is B 2[10−42−13]Converting into echelon formR2→R2−2R1[10−40−111]No. of non-zero rows =rank of matrix=2

The Rank of $[\begin{matrix} 1 & 0 & - 4 2 & - 1 & 3 \end{matrix}]$ is

The correct option is B 2
$[\begin{matrix} 1 & 0 & - 4 2 & - 1 & 3 \end{matrix}]$
Converting into echelon form
$R_{2} \to R_{2} - 2 R_{1}$
$[\begin{matrix} 1 & 0 & - 4 0 & - 1 & 11 \end{matrix}]$
No. of non-zero rows $=$ rank of matrix
$= 2$