1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

Find a basis for the subspace of R* consisting of all vectors of the form (a, b, c, d) where c = a + 7b and d = a- 6b. (A) {(1, 0, 1, 1), (0, 1, 7, —6)}; (В) {(0, 1, 7, 1), (0, 1, 1, —6)} (С) {(1, 1, 0, 1), (1, 0, 7, —6)} (D) {(0, 1, 7, 1), (1, 1, 0, –6)} (E) {(1, 0, 7, 1), (0, 1, 1, –6)} (F) {(1, 1, 0, 1), (0, 1, 7, –6)} (G) {(1, 0, 1, 1), (1, 0, 7, —6)} (Н) {(1, 0, 7, 1), (1, 0, 1, —6)}

Find a basis for the subspace of Rª spanned by S. S = {(3, -2, -3, 6), (2, -2, -3, 6), (-1, 1, 1, –2), (-2, 2, 2, –3)}

Find a basis for the orthogonal complement of the subspace of R spanned by the vectors. V1 = (1,5, -5), v2 = (3, 14, 2), v3 = (1, 4, 12) The basis for the row space is W1 = ( 1 )