The rank of the matrix A = begin{bmatrix} 2 & | vedclass

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(C) To find the rank of the matrix,we convert it into row echelon form using elementary row operations:$\begin{bmatrix} 2 & 1 & 2 \ 1 & 0 & 1 \ 4 &

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$2$

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(C) To find the rank of the matrix,we convert it into row echelon form using elementary row operations:$\begin{bmatrix} 2 & 1 & 2 \ 1 & 0 & 1 \ 4 & 1 & 4 \end{bmatrix} \xrightarrow{R_1 \leftrightarrow R_2} \begin{bmatrix} 1 & 0 & 1 \ 2 & 1 & 2 \ 4 & 1 & 4 \end{bmatrix}$Now,apply row operations to create zeros in the first column:$\xrightarrow[R_3 ightarrow R_3 - 4R_1]{R_2 ightarrow R_2 - 2R_1} \begin{bmatrix} 1 & 0 & 1 \ 0 & 1 & 0 \ 0 & 1 & 0 \end{bmatrix}$Next,apply row operation to create zeros in the second column:$\xrightarrow{R_3 ightarrow R_3 - R_2} \begin{bmatrix} 1 & 0 & 1 \ 0 & 1 & 0 \ 0 & 0 & 0 \end{bmatrix}$The matrix is now in row echelon form. The number of non-zero rows is $2$.Therefore,the rank of the matrix is $2$.

The rank of the matrix $A = \begin{bmatrix} 2 & 1 & 2 \\ 1 & 0 & 1 \\ 4 & 1 & 4 \end{bmatrix}$ is

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