Rank of Matrix Calculator

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

Related calculators: Basis Calculator, Linear Independence Calculator

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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 $$$2$$$.

Answer

The rank of the matrix equals $$$2$$$A.