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
Find a basis for and the dimension of the subspace w of R4. W = {(3s - t, s, t, s): s and t are real numbers) (a) a basis for the subspace w of R4 (b) the dimension of the subspace W of R4
Problem #7: Find a basis for the subspace of R4 consisting of all vectors of the form (a, b, c, d) where c = a + 2b and Problem #7: Select $ Just Save Submit Problem #7 for Grading Problem #7| Attempt #1 Your Answer: Attempt#2 | Attempt#3 Your Mark:
(7) Consider the set W of vectors of the form | 4a + 36 1 0 a+b+c c-2a where a,b,c E R are arbitrary real numbers. Either describe W as the span of a set of vectors and compute dim W, or show that W is not a linear subspace of R. (8) Find a basis for the span of the vectors 16115 1-1/ 121, ܘ ܟ ܢܝ
5. The given vectors form a basis for a subspace W of R3 or R4. Apply the Gram- Schmidt Process to obtain an orthogonal basis for W 2 3 1 W1 = W2 W3
Problem 2: Consider the following 2-dimensional linear subspace of R3: X = {(a,b,c) ER’: a+b+c=0}. Define a linear map F: X X by setting F(a,b,c) = (20 – 3b+c, -3a + 2b+c, a +b – 2c). (a) Find the matrix A representing F with respect to the basis 21 = (1,0, -1), 22 = (0,1, -1). (b) Find the matrix A representing F with respect to the basis î1 = (3,1,-4), f2 = (1, -2,1). (c) Find an invertible matrix...
5. The given vectors form a basis for a subspace W of R3 or R4. Apply the Gram- Schmidt Process to obtain an orthogonal basis for W 2 1 W1 = W2 = 3 -1 0 4. 1 , W3 = 1 2 1
5. (15 pts) Let 2 (a) Verify that W is a linear subspace of R4 1. (b) Find a basis for W
(c) Consider the subspace W R4 given by W = ER4 21 +12 + 24 = 0 and x2 + x3 + 14 = 0 14 Find an orthonormal basis H = {h1, h2, h3, h4} for R4 with the property that hy and h2 are elements of an orthonormal basis for W, where orth onormality is defined with respect to the dot product on R4 x R4
Consider the subspace W C R4 given by X1 X2 W = ER4 X1 + x2 + x4 = 0 and x2 + x3 + x4 = 0 X3 X4 = Find an orthonormal basis H {h1, h2, h3, h4} for R4 with the property that hy and h2 are elements of an orthonormal basis for W, where orthonormality is defined with respect to the dot product on R4 x R4.