Question

Determine whether the set S of vectors is linear independent or not: S = {u1, u2, u3, u4} ⊆ R^4, where u1, u2, u3, u4 are all different and it is known that (1, 0, 0, 0) is not a member of

Answer 1

We know that

$K=$ $(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1) )$ is a basis of $\R^4.$ Again we know that

any four linearly independent vector is a basis of $\R^4$ and

these vectors are equivalent to $K$ .

Vectors in the given set $S=$ $\{u_1,u_2,u_3,u_4 \}$ are all distinct and (1,0,0,0) does not belong to the equivalent of this set .

Hence ,the given set of vectors is $S$ not equivalent to $K$

Therefore, the given set of vectors is not linearly independent.