Question

What is the rank of a matrix with example?

Answer 1

Rank of matrices: The maximum number of linearly independent columns (or rows ) of a matrix is called the rank of a matrix.

Example:

$A=\left[\begin{array}{ccc}1& 2& 4\\ 3& 5& 12\\ 2& 4& 7\end{array}\right]$

Apply $R_2\to R_2-3R_1$ and $R_3\to R_3-2R_1$, we get

$A=\left[\begin{array}{ccc}1& 2& 4\\ 0& -1& 0\\ 0& 0& -1\end{array}\right]$

The matrix is in echelon form and there are $3$ non-zero rows present in it.

Hence, the rank of the matrix $A$ is $3$.