## Determine a Condition on $a, b$ so that Vectors are Linearly Dependent

## Problem 563

Let

\[\mathbf{v}_1=\begin{bmatrix}

1 \\

2 \\

0

\end{bmatrix}, \mathbf{v}_2=\begin{bmatrix}

1 \\

a \\

5

\end{bmatrix}, \mathbf{v}_3=\begin{bmatrix}

0 \\

4 \\

b

\end{bmatrix}\]
be vectors in $\R^3$.

Determine a condition on the scalars $a, b$ so that the set of vectors $\{\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3\}$ is linearly dependent.

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