Can you please help me with this? And can you please explain the answers to me? Please do not use cursive as I can't read that.

Let S = span fal - : -- - - [ : 1 (a) Use Gram-Schmidt process to find an orthogonal basis {u', u', u} } of S. (b) Find an orthonormal basis {ql, q2, q3} of S. 2. Let S = span {al = (a) Use Gram-Schmidt process to find an orthogonal basis ful, u?} of S. (b) Find an orthonormal basis {q', q? } of S. (c) Find a unit vector q3 such that Q = [q q q3] is a 3 x 3 orthogonal matrix. -3 0 3. Let A = 2 1 2 3 (a) Compute det(A) using the cofactor expansion along 2nd row. (b) Compute det(A) using the cofactor expansion along 3rd column. 0 2 4. Compute det (A), where A = 2 0 0 0 0 0 5. Let A and B be two 4 x 4 matrices and let det(A) = -2 and det (B) = 8. Let C = 243B-1. Find det (C). 109 6. Let A = 0 where a is a scalar. Show that det( A) is independent of a. 3 7. Let A, B and C be n x n matrices and let D = ABC. Prove that if D is nonsingular, then A, B and C must be nonsingular