## Determine Conditions on Scalars so that the Set of Vectors is Linearly Dependent

## Problem 279

Determine conditions on the scalars $a, b$ so that the following set $S$ of vectors is linearly dependent.

\begin{align*}

S=\{\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3\},

\end{align*}

where

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

1 \\

3 \\

1

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

1 \\

a \\

4

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

0 \\

2 \\

b

\end{bmatrix}.\]

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