Question

Why does the vector not form a basis for the indicated vector space? v_1=(1,1,1) v_2=(-1,2,4) v_3=(0,7,9) and v_4(-9,8,6)

Answer 1

Is the matrix for this [1 -1 0 -9; 1 2 7 8; 1 4 9 6]? Or [1 1 1; -1 2 4; 0 7 9; -9 8 6]?

Answer 2

Simply show that the set of vectors is not linearly independent. This will contradict that it is a basis.

Answer 3

Yes row reduction or column reduction should work.

Answer 4

So it doesn't matter which way I write the matrix?

Answer 5

I would usually write each vector as a column.

Answer 6

In any case, theoretically its clear, since the dimension of the vector space is 3, it would be impossible for a basis to have more than 3 vectors. So already by the theory it is clear that the set of vectors does not form a basis for the vector space.

Answer 7

Okay but if do it with a vector as rows I get [1 0 0; 0 1 0; 0 0 1; 0 0 0]

Answer 8

this is not linearly independent right? b/c of the last zero row?

Answer 9

Yeah

Answer 10

alright thanks for your help

Answer 11

quick way: the standard basis has 3 vectors...you have 4...therefore it cannot be a basis

Answer 12

hey joe i need your help