4. Find an orthogonal basis of the subspace W of R5 spanned by {ū₁ = (1, 1, 1, 0, 1), 2 = (1, 0, 0, -1, 1), ū3 = (3, 1, 1, -2, 3), 4 = (0, 2, 1, 1, -1)}

Please two only

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 orthogonal complement of the subspace of Rª spanned by the following vectors. V1 = (1,-1,7,3), V2 = (2,-1,5,2), V3 = (1, 0, -2, -1) The required basis can be written in the form {(x, y, 1, 0), (z, w, 0, 1)}.