Rank of Matrix Calculator

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

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

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.