Row Space of Matrix Calculator

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

Related calculator: Column Space of Matrix Calculator

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 row space of $$$\left[\begin{array}{ccc}1 & 1 & 0\\2 & 3 & -2\\-1 & -4 & 6\end{array}\right]$$$.

Solution

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

The row space is a space spanned by the nonzero rows of the reduced matrix.

Thus, the row space is $$$\left\{\left[\begin{array}{c}1\\1\\0\end{array}\right], \left[\begin{array}{c}0\\1\\-2\end{array}\right]\right\}$$$.

Answer

The row space of the matrix is $$$\left\{\left[\begin{array}{c}1\\1\\0\end{array}\right], \left[\begin{array}{c}0\\1\\-2\end{array}\right]\right\}$$$A.