#6. Let W be the subspace of R³ spanned by the two vectors (1, – 1,1) and (3, – 2,0).Which one of the following vectors is a basis for W, the orthogonal complement of W?(A) (1, 1, 0) (B) (- 1,0, 1) (C) (1, 2, 1) (D) (2, 3,0) (E) (2, 3, 1)

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Answered: #6. Let W be the subspace of R³ spanned…

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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4] Show that the following sets of vectors are linearly dependent in R3. (c) {{5, 2, -3), (3, 0, 4), (-3, 0, -4)} (d) {{1, 1, 1), (2, 2, 2), (0, 1, 5)}
1. Determine whether the vectors (1,-1) and (1, 1)T are linearly inde- pendent or not. 2. Show that the vectors (1,0,0), (1, 1, 0) and (1,1,1) form a basis of R³. 3. Suppose that the vectors (1, 2, -1,0) and (1,3,2,0) span the sub- space U of R4. Determine whether the vector (1, 1, 1, 0) belongs to U or not.
just b)
PLEASE MAKE ANSWER CLEAR TO READ!!!! (SHOULD BE 2 MATRIXs)
I need help with both parts using the matrix way
4 Let W = span(vV1, V2) where vi = and v2 2 . Then: (a) Find the orthogonal decomposition of the vector x = 3 (b) Find an orthogonal basis for W- (remember to justify your answer).
Consider the subspace S of the Euclidean inner product space R+ spanned by the vectors v₁ = (1,1,1,1), v₂=(1,1,2,4), v₂=(1,2,-4,-3). Find an orthogonal basis of S. O*((-.-3.1).(1.2.-4,-3).(4,2,1,1)) OB. © ³ {(1,1,2,4), ( − 1, − 1,0,2 A. -1,0,2), (12. 2.-3,1)} O C. None in the given list. OD. {(1,1,1,1),(1,1,2,4), (1,2,-4,-3) } OE {(1,1,1,1),(-1,-1,0,2), (1,3, -6,2) }
4. Vector u is a unit vector orthogonal to vectors a and b, where a = i+j-k, b=2i-j. Then the coordinates of vector u in the basis {i, j,k} are 2 3 (a) (b) (-1, 2,–3) (c) None of the above is true
(3,0,0), v2 = (1,2,0), and v3 = a) Are the vectors linearly independent or linearly dependent? Given vectors v, = (2, –4,5). b) Do the vectors form a basis for R3? Why or why not?
Let { u1, U2, Uz, U4, U5} be an orthogonal basis for R5 , y a vector in R5 , W1 Span { u1, Uz} and W2 Span { u3, U4, U5} . Which of the following is False? %| (a) W1 = W2" (b) W2 = W1 (c) There are two vectors z1in W1 and zzin W2such that y = z1+ Z2 (d) y is orthogonal to W1 and W2. %3D
Find a basis for the subspace of R° that is spanned by the vectors V1 = (1,0, 0), v2 = (1, 0, 1), v3 = (2, 0, 1), v4 = (0, 0, -2) Vị and v2 form a basis for span {V1, V2, V3, V4}. V1 and v3 form a basis for span {v1, V2, V3, V4}. V2 and v4 form a basis for span {v1, V2, V3, V43. V1 and v4 form a basis for span {v1, V2, V3, V4}. V2 and v3 form a basis for span {v1, V2, V3, V43. V3 and v4 form a basis for span {v1, V2, V3, V4}. O All of the above are correct.

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#6. Let W be the subspace of R³ spanned by the two vectors (1, – 1,1) and (3, – 2,0). Which one of the following vectors is a basis for W, the orthogonal complement of W? (A) (1, 1, 0) (B) (- 1,0, 1) (C) (1, 2, 1) (D) (2, 3,0) (E) (2, 3, 1)