## Find Bases for the Null Space, Range, and the Row Space of a $5\times 4$ Matrix

## Problem 604

Let

\[A=\begin{bmatrix}

1 & -1 & 0 & 0 \\

0 &1 & 1 & 1 \\

1 & -1 & 0 & 0 \\

0 & 2 & 2 & 2\\

0 & 0 & 0 & 0

\end{bmatrix}.\]

**(a)** Find a basis for the null space $\calN(A)$.

**(b)** Find a basis of the range $\calR(A)$.

**(c)** Find a basis of the row space for $A$.

*(The Ohio State University, Linear Algebra Midterm)*

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