Question

Let V be a vector space, and let v1, v2, v3 and v4 be linearly independent vectors in V . In parts (a) and (b) below, determine whether each of the given sets of vectors is linearly independent or linearly dependent. Prove your answers using the definition.

u1 = v1 − 7v3, u2 = v1, u3 = v3, u4 = v3 + v4.

Answer 1

Explanation:

`u_3 = v_3` and
`u_2 = v_1`

`u_1= v_1 -7 v_3`

Replace the first line to the second line, you have
`u_1= u_2-7u_3`

That shows
`\{u_1, u_2, u_3,u_4\}`

is not linear independent.