The rank of the following matrix A is A = beg | vedclass

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(B) Given matrix $A = \begin{bmatrix} 1 & -2 & 3 & -4 \ 2 & 9 & 4 & 5 \ 4 & 5 & 10 & -3 \ 1 & 11 & -1 & 9 \end{bmatrix}$ Apply row operations to re

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$3$

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(B) Given matrix $A = \begin{bmatrix} 1 & -2 & 3 & -4 \ 2 & 9 & 4 & 5 \ 4 & 5 & 10 & -3 \ 1 & 11 & -1 & 9 \end{bmatrix}$ Apply row operations to reduce the matrix to row-echelon form: $R_2 ightarrow R_2 - 2R_1$ gives $\begin{bmatrix} 1 & -2 & 3 & -4 \ 0 & 13 & -2 & 13 \ 4 & 5 & 10 & -3 \ 1 & 11 & -1 & 9 \end{bmatrix}$ $R_3 ightarrow R_3 - 4R_1$ gives $\begin{bmatrix} 1 & -2 & 3 & -4 \ 0 & 13 & -2 & 13 \ 0 & 13 & -2 & 13 \ 1 & 11 & -1 & 9 \end{bmatrix}$ $R_4 ightarrow R_4 - R_1$ gives $\begin{bmatrix} 1 & -2 & 3 & -4 \ 0 & 13 & -2 & 13 \ 0 & 13 & -2 & 13 \ 0 & 13 & -4 & 13 \end{bmatrix}$ $R_3 ightarrow R_3 - R_2$ gives $\begin{bmatrix} 1 & -2 & 3 & -4 \ 0 & 13 & -2 & 13 \ 0 & 0 & 0 & 0 \ 0 & 13 & -4 & 13 \end{bmatrix}$ $R_4 ightarrow R_4 - R_2$ gives $\begin{bmatrix} 1 & -2 & 3 & -4 \ 0 & 13 & -2 & 13 \ 0 & 0 & 0 & 0 \ 0 & 0 & -2 & 0 \end{bmatrix}$ The number of non-zero rows in the row-echelon form is $3$. Therefore,the rank of matrix $A$ is $3$.

The rank of the following matrix $A$ is
$A = \begin{bmatrix} 1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 4 & 5 & 10 & -3 \\ 1 & 11 & -1 & 9 \end{bmatrix}$

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The rank of the following matrix $A$ is $A = \begin{bmatrix} 1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 4 & 5 & 10 & -3 \\ 1 & 11 & -1 & 9 \end{bmatrix}$