Let S be =
and let W be the subspace spanned by S.
=
Is in W? If so find a linear combination of the vectors in S Which adds up to U
So i know that i am trying to find r1, r2, r3, r4, such that
So i found the reduced row echelon form of the matrix and this is what i got
column 1 is x1 column 2 is x2 .... etc.
From this i can see that the 3rd column is free which shows that there are infinitely many solutions. So YES U is in W because the system has at least one solution.
so i paramaterized the solutions and set....
x3 = y
x1 + x3 = 2
x2 + x3 = 1
x4 = 1
so
x1 = 2-y
x2 = 1-y
x3 = y
x4 = 1
y can be any real # so... if y=1 then
r1 = 1
r2 = 0
r3 = 1
r4 = 1
This ^^ is one linear combination of the vectors in S that adds up to U
Did i do all this right? I just want to check. Thanks for looking it over and commenting on anything