6. Let S : {uh 11?, us, u4} be a set in R4. After performing the Gram-Schmidt process on S, v4 2 0, but v1 7E (1V; # 0, and V3 7E 0. Which oflhe following statements is true? (i mark) span(S)is a 3~dimensional subspace. The set S is linearly independent. {v1,v2,v3, v4} can be normalized to create an orthonormal set. 7. Suppose OHOH spans a subspace V . Which of the following vectors are orthogonal to V? O (1 mark) O N HK O O O8. Let V = y ac + 2y - z=0 = span and p = 2 COLA . Let n = u - p = Coll Which of HO the following statements are true? (1 mark) u is orthogonal to V. O u is in V. P is the orthogonal projection of u onto V. n is in V. p is in V. n is orthogonal to V.9' Let V be the plane in R3 satisfying the equation a: 7 239 + 33 : 0. Let W : {w E R3|W is orthogonal to V}. Which of the following statements is true? (i mark) W is the line in R3passing through the origin and the point (1, 1,1). W is not a subspace of R3. W is the line in R3passing through the origin and the point (1, *2, 3). W is a plane in R3 passing through the origin. 10. Let u1, . . ., ux be row vectors in ". Let V = span ful, . .., ux} and W = {w E R" |w is orthogonal to V}. If A is the matrix whose rows are U1, . . .; Up, then W is the nullspace of A. (1 mark) O True O False