Is my basis different because there are infinitely many solutions for this problem and I just happened to find another one? Thanks, for all the help by the way!
EDIT:
To show if the two vectors are in the linear span of the two vectors do I just take:
c1[16; 4; 21; 0] + c2 [1; 2; 0; 7] = [1...
Plugging in [1, -4, 0, 1; 5 1 -4 -1] in wolfram|alpha and having it row reduce the matrix gave me [1, 0, -16/21, -1/7; 0 1 -4/21, -2/7].
Doing the calculations again I get the free variables x3 and x4 with x3[16/21; 4/21; 1; 0] and x4[1/7; 2/7; 0; 1].
Scaling these vectors doesn't get me...
I'm getting x3[0; 4/21; 1; 0] and x4[-1; 6/21; 0; 1], but the answer is [4; 0; 6; -4], [0; 4; -3; 16]. I've done the calculation several times and I keep getting the same answers.
EDIT:
I got to those vectors by transposing W, resulting in:
[1, -4, 0, 1; 5 1 -4 -1]. After that I row reduced...
Homework Statement
Let W be a subspace of ℝ4 spanned by the vectors:
u1 = [1; -4; 0; 1], u2 = [7; -7; -4; 1]
Find an orthogonal basis for W by performing the Gram Schmidt proces to there vectors. Find a basis for W perp (W with the upside down T).
Homework Equations
Gram...