# Rank of Matrix Calculator

The calculator will find the rank of the matrix, with steps shown.

Related calculators: Basis Calculator, Linear Independence Calculator

## Your Input

**Find the rank of $$$\left[\begin{array}{ccc}1 & 2 & 3\\2 & 5 & 7\\4 & 9 & 13\end{array}\right]$$$.**

## Solution

The row echelon form of the matrix is $$$\left[\begin{array}{ccc}1 & 2 & 3\\0 & 1 & 1\\0 & 0 & 0\end{array}\right]$$$ (for steps, see rref calculator).

The rank of a matrix is the number of nonzero rows in the reduced matrix, so the rank is $$$2$$$.