Rank of a matrix:

Rank of a Matrix: Let M be a non-zero matrix. If r is the number of non-zero rows when it is
reduced to the reduced echelon form, then r is called the (row) rank of the matrix M.

Example:

Find rank the rank of matrix [katex]\begin{bmatrix}
1 &-1 &2 &-3 \\
2 &0 &7 &-7 \\
3 &1 &12 &-11
\end{bmatrix} [/katex]

Solution:

[katex]\begin{bmatrix}
1 &-1 &2 &-3 \\
2 &0 &7 &-7 \\
3 &1 &12 &-11
\end{bmatrix}[/katex]

[katex]R\begin{bmatrix}
1 &-1 &2 &-3 \\
0 &2 &3 &-1 \\
0 &4 &6 &-2
\end{bmatrix}[/katex]

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