Let W be the subspace of R4 which is spanned by the vectors v₁ = (1, 0,-1,2), v2 = (2,0,0,2), V3 = = (1, 1, 1,3). Which of the following statements are true? (i) The set Bw = {v₁, v2, v3} is a basis for W. (ii) The set Cw = {(1,0,1,0), (1, 0, -1, 2)} is an orthogonal basis for W. (iii) The orthogonal projection of (1,1, 1, 1) onto W.is p = 5177 62'6'6 (iv) Bw = {(-1, -3, 1, 1), (-1,1, 1, 1)} is a basis for the orthogonal com- plement W of W. (v) The set By = {(1, 0,-1,2), (2,0, 0, 2), (1, 1, 1, 3), (-1, -3, 1, 1)} is a ba- sis for V = R4. O A) (ii) and (iv) OB)(), (i), (iv). and (v) C) (i), (i) and (iv) OD) (). (iv) and (v) OE) 0) () and (v)
Let W be the subspace of R4 which is spanned by the vectors v₁ = (1, 0,-1,2), v2 = (2,0,0,2), V3 = = (1, 1, 1,3). Which of the following statements are true? (i) The set Bw = {v₁, v2, v3} is a basis for W. (ii) The set Cw = {(1,0,1,0), (1, 0, -1, 2)} is an orthogonal basis for W. (iii) The orthogonal projection of (1,1, 1, 1) onto W.is p = 5177 62'6'6 (iv) Bw = {(-1, -3, 1, 1), (-1,1, 1, 1)} is a basis for the orthogonal com- plement W of W. (v) The set By = {(1, 0,-1,2), (2,0, 0, 2), (1, 1, 1, 3), (-1, -3, 1, 1)} is a ba- sis for V = R4. O A) (ii) and (iv) OB)(), (i), (iv). and (v) C) (i), (i) and (iv) OD) (). (iv) and (v) OE) 0) () and (v)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let W be the subspace of R4 which is spanned by the vectors
v₁ = (1, 0,-1,2), v₂ = (2,0, 0, 2), v3 = (1, 1, 1, 3).
Which of the following statements are true?
(i) The set Bw = {v₁, v2, v3} is a basis for W.
(ii) The set Cw = {(1,0, 1,0), (1,0,-1,2)} is an orthogonal basis for W.
(iii) The orthogonal projection of (1, 1, 1, 1) onto W.is p =
5 1 77
62'6'6
(iv) Bw = {(-1, -3, 1, 1), (-1, 1, 1, 1)} is a basis for the orthogonal com-
plement W of W.
(v) The set By = {(1, 0, -1, 2), (2, 0, 0, 2), (1, 1, 1, 3), (−1, −3, 1, 1)} is a ba-
sis for V = R¹.
O
A) (III) and (iv)
B) (1), (i), (iv), and (v)
C) (I), (II) and (iv)
D) (i), (iv), and (v)
E) (0) (i) and (v)
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