21412. Let u= 1-------BW = 2201V =33=21(a) Are u', v, w, and x' linearly independent?(b) Do u and x span the entire R³?(c) Are u, V, and x' linearly independent?Do theyform(d) Are v, w, and x linearly independent? Do they forma basisa basisEngof R³?of R³?

Answered: Image /qna-images/answer/213addc7-f591-4de0-9a62-e63e5a2035d9.jpg

Answered: 2. Let u = W = 2 ----- V 1 = = 3 2 1…

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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(b) Is the following set of vectors S basis for vector space V? Where (i) S = {(1,2), (0, 3), (1, 5)} and V = R? (ii) S = {(-1,3, 2), (6, 1, 1)} and V = R³ If not explain the reason.
Explain why S is not a basis for R2. S = {(2, 5), (6, 15)} O sis linearly dependent. O S does not span R2. O is linearly dependent and does not span R2.
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
7. Find the coordinates of the vector v relative to the ordered basis B. a) B = {x² + 2x + 2, 2x + 3,−x² + x + 1} v=-3x² + 6x + 8 14 D b) B = {[1₁¹] [ = (₁ 3²1 -CAC) = B₂ -QAED = 0 v= c) B₁ v= 22
a) Find , \pl, d (p, q), and then find the angle between them for the polynomials in P2 if p(x) = -3x² + 2x – 5 , and q(x) = -x+5x? b) Verify that the basis set S = {(3,0,4), (-4,0,3), (0,1,0)} is orthogonal then find the coordinates of the vector u = (-5,5,1) using inner product
(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?
3. Let T = 1 7 W= 1 and x = 0 (a) Are vectors u, V, and w linearly independent? (b) Do u, v', and w span the entire R³? (c) Do u, v', and w form a basis of R³? abc po
b
: Let S = {v1, v2}, where v = standard vectors when added to the set S produces a basis for R? (6,-5, 7,-1) and v2 = (-12, 20, -28, 4). Which of the following combination of (A) v3 = (1, 0, 0, 0), v4 = (0, 0, 1, 0) and vs = (0, 0, 0, 1) (B) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0, 0, 0, 1) (C) v3 = (1, 0, 0, 0) and v4 = (0, 0, 0, 1) (D) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0. 0, 1, 0) (E)v3 = (1, 0, 0, 0) and v4 = (0, 1, 0, 0) (F) v3 = (1, 0, 0, 0) and v4 = (0, 0, 1, 0) (G) v3 = (0, 1, 0, 0) and v4 = (0, 0, 0, 1) %3D %3D (H) v3 = (0, 1, 0, 0), v4 = (0, 0, 1, 0) and vs = (0. 0, 0, 1) %3D
The coordinate vector of the vector (1,2,2) in the basis B = {u= (1,1,1); v = (1,0,1); w= (0,0,1) } is : O A. (1,2,2) O B. (2,-1,1) O C. (2,1,3) O D. (1,2,1)

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2. Let u = W = 2 ----- V 1 = = 3 2 1 Ene 0 3 (a) Are u, v, w, and x linearly independent? (b) Do u and X span the entire R³? V form a basis of R³? (c) Are u', V, and x linearly independent? Do they (d) Are V, W, and x linearly independent? Do they form a basis of R³?