Why is this statement about $\text{Span}$ false?

Question

Here is a true-false question known to be false:

If $\mathbf{a}$ is in $\text{Span} \left \{ \mathbf{b}, \mathbf{c} \right \}$, then $\mathbf{b}$ is in $\text{Span}\left\{\mathbf{a},\mathbf{c}\right\}$.

Why is it false? Have I forgotten to consider some edge cases?

Let $\mathbf a=\mathbf c$ and figure out the rest. – Git Gud Sep 29 '14 at 02:25 — Git Gud, Sep 29 '14 at 02:25

score 3 · Accepted Answer · answered Sep 29 '14 at 02:25

3

$\mathbf{a}$ may be a scalar multiple of $\mathbf{c}$, and independent of $\mathbf{b}$.

answered Sep 29 '14 at 02:25

Michael Hardy

1

Why is this statement about $\text{Span}$ false?

1 Answers1