## How to Find a Basis for the Nullspace, Row Space, and Range of a Matrix

## Problem 708

Let $A=\begin{bmatrix}

2 & 4 & 6 & 8 \\

1 &3 & 0 & 5 \\

1 & 1 & 6 & 3

\end{bmatrix}$.

**(a)** Find a basis for the nullspace of $A$.

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

**(c)** Find a basis for the range of $A$ that consists of column vectors of $A$.

**(d)** For each column vector which is not a basis vector that you obtained in part (c), express it as a linear combination of the basis vectors for the range of $A$.