- #1

- 721

- 1

## Homework Statement

Let V be a real vector space and [tex]{b_1,b_2,b_3,b_4}[/tex] a linearly independent set of vectors in V

Is the set [tex]\left \{ b_1,b_2,b_3,b_1+b_4,b_2+b_4 \right \}[/tex]

## The Attempt at a Solution

[tex]\alpha_1b_1+\alpha_2b_2+\alpha_3b_3+\alpha_4\left \{ b_1+b_4 \right \}+\alpha_5\left \{ b_2+b_4 \right \} =0[/tex]

Rearranging

[tex]b_1(\alpha_1+\alpha_4)+b_2(\alpha_2+\alpha_5)+b_3(\alpha_3)+b_4(\alpha_4+\alpha_5)=0[/tex]

Hence it is NOT linearly independant since the scalars are all not 0.....?