# Why is this linearly independent?

1. Homework Statement

Determine whether the given vector functions are linearly dependent or independent on the interval $$(-\infty, \infty)$$

$$\begin{pmatrix} t \\ 3 \end{pmatrix}, \begin{pmatrix} 4 \\ 1 \end{pmatrix}$$

2. Homework Equations

3. The Attempt at a Solution

I computed the wronskian to be t-12. Since the wronskian is 0 at t=12, shouldn't this be linearly dependent? The book says that this is linearly independent. Why is that?

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The functions are only linearly dependent if the Wronskian is zero on the whole interval

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