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## Homework Statement

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

## The Attempt at a Solution

Show that the span [itex](b_1,b_2,b_3,b_4)=span(b_1-b_3,b_2-b_1,b_3,b_4-b_2)[/itex]

If I equate the LHS and RHS as

[itex]\alpha_1b_1=+\alpha_1b_1-\alpha_3b_3[/itex] implies [itex]\alpha_3=0[/itex]

[itex]\alpha_2b_2=\alpha_2b_2-\alpha_1b_1[/itex] implies [itex]\alpha_1=0[/itex]

[itex]\alpha_3b_3=\alpha_3b_3[/itex] but [itex]\alpha_3=0[/itex]

[itex]\alpha_4b_4=\alpha_4b_4-\alpha_2b_2[/itex] implies [itex]\alpha_2=0[/itex]

This correct? What about [itex]\alpha_4[/itex]?