## Given a Spanning Set of the Null Space of a Matrix, Find the Rank

## Problem 303

Let $A$ be a real $7\times 3$ matrix such that its null space is spanned by the vectors

\[\begin{bmatrix}

1 \\

2 \\

0

\end{bmatrix}, \begin{bmatrix}

2 \\

1 \\

0

\end{bmatrix}, \text{ and } \begin{bmatrix}

1 \\

-1 \\

0

\end{bmatrix}.\]
Then find the rank of the matrix $A$.

(*Purdue University, Linear Algebra Final Exam Problem*)

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