Question

Determine whether S is a basis for R³.

S = {(4, 2, 5), (0, 2, 5), (0, 0, 5)}

S is a basis for R³.S is not a basis for R³.    

If S is a basis for R³, then write u = (8, 2, 15) as a linear combination of the vectors in S. (Use s₁, s₂, and s₃, respectively, as the vectors in S. If not possible, enter IMPOSSIBLE.)

u =

Answer 1

Solution: Given:

To show:   is a basis of

Let   

Consider   

  Any vector in   can be written as a linear combination of vectors in

To check:   is linearly independent

Consider   

      is linearly independent

  is a basis of

To show: is a linear combination of vectors in

Put   in