Explain why you can be certain without calculations that the

Explain why you can be certain, without calculations, that the set below must be linearly dependent in IR2:

Solution

Three vectors u, v, w are linearly dependent if

au+bv+cw =0 for non zero a, ,b ,c.

Here we have 3 vectors with 2 entries each .

So if we use au+bv+cw =0 then we will be having only 2 equations with 3 unknowns a, b, c

to solve for.

Which suggests that there can be many non zero a, ,b, c which would satisfy these equations.

Hence we can say with certainty that these vectors are linearly dependent.