Use the Gram-Schmidt procedure to find an orthonormal basis for the following subspace of R4.  W = {(w1 w2 w3 w4), w1 - w2 - 2w3 + w4 = 0}

Consider the subspaces U = {(a, b, c, d) : b – 2c+d = 0} and W = {(a, b, c, d) : a = d, b = 2c} of R*. Find a basis and the dimensi on of (a) U, (b) W, (c) UnW.

: Let W be the subspace of R* spanned by the vectors (1, 0, 1, 0), u2 (0, —1, 1, 0), and uз — (0, 0, 1, –1). Use the Gram-Schmidt process to transform the basis {u1, u2, u3} into an orthonormal basis. (A) vI = (E.0.. 0), v2 = (B) v| = (E, 0, , 0), v3 = ( 6, v6, vo 0), v3 = (E,. (-V6, -V6, v6,0), v3 = (-V5, V3 v3 và V2 = (C) vị = ( .0, 2, 0), v2 = (e, Ye, v, 0), v3 = (D) v - (E.0.. 0). v2 - (- NE 0), v3 ( ) v2 = (- о). (E) v = (-.0, , 0). () vi = (-E. 0, 0), vz = ( , 0), vs (G) v, = (E.0., 0), v2 = (-, NG, 0), v3 = (V6, N6, V6 0), v3 = V3 V3 V2 o). _V6 Vo V3 V3 V2 V3 о). 6. (H) Vị 0). V3 V3 V3 V3 V2 = V3 3 6. 6.

Let W be the subspace of R* spanned by the vectors uj = (1,0, 1,0), u2 = (0, 1, 1,0), and uz = (0,0, 1,–1). Use the Gram-Schmidt process to transform the basis {u1, u2, u3} into an orthonormal basis.

Let U be the subspace of C5 given by U = {(21, 22, 23, 24, 25) | 621 = 22 and 23 +224 + 3z5 = 0}. (a) Find a basis of U. (b) Extend the basis in part (a) to a basis of C5. (c) Find a subspace W of C5 such that C5 = U@W.

The vector x is in a subspace H with a basis ß = {b₁,b2}. Find the ß-coordinate vector of x. b₁ = [+] °4 °H [1] O = X =