The rank of the matrix left[begin{array}{cccc | vedclass

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(B) Let $A = \left[\begin{array}{cccc}3 & 2 & 1 & -4 \ 2 & 3 & 0 & -1 \ 1 & -6 & 3 & -8\end{array}ight]$.Applying row operations to reduce the mat

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$2$

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(B) Let $A = \left[\begin{array}{cccc}3 & 2 & 1 & -4 \ 2 & 3 & 0 & -1 \ 1 & -6 & 3 & -8\end{array}ight]$.Applying row operations to reduce the matrix to row-echelon form:Perform $R_2 ightarrow R_2 - \frac{2}{3}R_1$ and $R_3 ightarrow R_3 - \frac{1}{3}R_1$:$A \sim \left[\begin{array}{cccc}3 & 2 & 1 & -4 \ 0 & 5/3 & -2/3 & 5/3 \ 0 & -20/3 & 8/3 & -20/3\end{array}ight]$Next, apply $R_3 ightarrow R_3 + 4R_2$:$A \sim \left[\begin{array}{cccc}3 & 2 & 1 & -4 \ 0 & 5/3 & -2/3 & 5/3 \ 0 & 0 & 0 & 0\end{array}ight]$The number of non-zero rows in the row-echelon form is $2$.Therefore, the rank of the matrix $A$ is $2$.

The rank of the matrix $\left[\begin{array}{cccc}3 & 2 & 1 & -4 \\ 2 & 3 & 0 & -1 \\ 1 & -6 & 3 & -8\end{array}\right]$ is

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