# Search results

1. ### Finding the basis for W perp

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...
2. ### Finding the basis for W perp

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...
3. ### Finding the basis for W perp

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...
4. ### Finding the basis for W perp

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...
5. ### Linear Algebra: Orthogonal Projections

Hey first time poster here. Homework Statement Find the orthogonal projection projWy u1 = [-1; 3; 1; 1], u2 = [3; 1; 1; -1], u3 = [-1; -1; 3; -1], y = [1; 0; 0; 1] where {u1, u2, u3} is an orthogonal basis. Homework Equations yhat = [dot(y,U1)/dot(U1,U1)]U1 + ...