(B) Let $A = \left[\begin{array}{ccc} 2 & 1 & 1 \\ 0 & 3 & -1 \\ 1 & -1 & 1 \end{array}\right]$.Applying row operation $R_3 \rightarrow 2R_3 - R_1$:$A

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(B) Let $A = \left[\begin{array}{ccc} 2 & 1 & 1 \\ 0 & 3 & -1 \\ 1 & -1 & 1 \end{array}\right]$.Applying row operation $R_3 \rightarrow 2R_3 - R_1$:$A \sim \left[\begin{array}{ccc} 2 & 1 & 1 \\ 0 & 3 & -1 \\ 0 & -3 & 1 \end{array}\right]$.Applying row operation $R_3 \rightarrow R_3 + R_2$:$A \sim \left[\begin{array}{ccc} 2 & 1 & 1 \\ 0 & 3 & -1 \\ 0 & 0 & 0 \end{array}\right]$.Since there are $2$ non-zero rows in the row-echelon form,the rank of $A$ is $2$.Therefore,option $(b)$ is correct.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Rank of Matrices , Some special determinants, differentiation and integration of determinants

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The rank of $\left[\begin{array}{ccc}2 & 1 & 1 \\ 0 & 3 & -1 \\ 1 & -1 & 1\end{array}\right]$ is

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$1$
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$2$
C
$3$
D
$4$

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3 and 4 .Determinants and Matrices

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Rank of Matrices , Some special determinants, differentiation and integration of determinants

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The rank of $\left[\begin{array}{ccc}2 & 1 & 1 \\ 0 & 3 & -1 \\ 1 & -1 & 1\end{array}\right]$ is

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