Row Space Calculator
Calculate the row space of a matrix step by step
The calculator will find the row space of the matrix, with steps shown.
Related calculator: Column Space Calculator
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 reduced row echelon form of the matrix is $$$\left[\begin{array}{ccc}1 & 0 & 2\\0 & 1 & -2\\0 & 0 & 0\end{array}\right]$$$ (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 $$$\left\{\left[\begin{array}{c}1\\0\\2\end{array}\right], \left[\begin{array}{c}0\\1\\-2\end{array}\right]\right\}$$$.
Answer
The row space of the matrix is $$$\left\{\left[\begin{array}{c}1\\0\\2\end{array}\right], \left[\begin{array}{c}0\\1\\-2\end{array}\right]\right\}$$$A.