Question

Find a basis for the subspace of R4 consisting of all vectors of the form (a, b, c, d)  where  c  =  a + 4b  and  d  =  a − 6b. Problem #7 : Find a basis for the subspace of R4 consisting of all vectors ofthe form (a, b, c, d) where c a + 4b and d=a-6b

Answer 1

W = { (a, b, c, d): C = a + 4b, d = a - 6b} a, b, c, d elementof 1R] Now (a, b, c, d) = (a, b, a + 4b, a - 6b) [therefore C = a + 4b, d = a - 6b) Now (a, b, a + 4b, a - 6b) = a(1, 0, 1, 1) + b(0, 1, 4, - 6) Hence basis of W B = {(1, 0, 1, 1) , (0, 1, 4, -6)}