SOLUTION: let v1=(-3,2,4), v2=(-3,5,0), and y=(-18,24,h) for what value of h is y in the plane spanned by v1 and v2?

Algebra ->  Matrices-and-determiminant -> SOLUTION: let v1=(-3,2,4), v2=(-3,5,0), and y=(-18,24,h) for what value of h is y in the plane spanned by v1 and v2?      Log On


   

Question 465677: let v1=(-3,2,4), v2=(-3,5,0), and y=(-18,24,h)
for what value of h is y in the plane spanned by v1 and v2?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The matrix %28matrix%283%2C3%2C+-3%2C-3%2C-18%2C2%2C5%2C24%2C4%2C0%2Ch%29%29 must have rank less than 3.
After reducing to row echelon form, the matrix becomes %28matrix%283%2C3%2C+1%2C1%2C6%2C0%2C1%2C4%2C0%2C0%2C%288-h%29%2F4%29%29%29%29.
==> h = 8 for linear dependence.
==> y is in the plane spanned by v1 and v2 if h = 8.