{[i :]:[1 00 0; :]:[: :)-[: :]}1 11 011- Let Ba basis for M2(R).=0 01 1Find the coordinate vector [A]B_ relative to the basis B, wherea b(a) A(а) А —с d-1 3(b) А —2 5

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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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Find the representation of (9, -2, -3) in each of the following ordered bases. Your answers should be vectors of the general form . a. Represent the vector (9, -2, -3) in terms of the ordered basis B = {i,j,k}. [(9,-2,-3)]B= b. Represent the vector (9, -2, -3) in terms of the ordered basis C = {3, e1, e2}. [(9,-2,-3)] c = c. Represent the vector (9, -2, -3) in terms of the ordered basis D= {-2, -1, e3}. [(9,-2,-3)]D =
B = {3 – 3x², 9 – 2x – 9x², 13 – 4x – 12x?} is a basis for P2. The coordinate vector of p(x) = 4 + 2x – 6x² relative to the basis B is [p]B =
2. Find the coordinate vector [x] of a relative to the given basis B = {b₁,b2, b3} . b₁ = -1 , b₂ = -3 4 9 b3 = 2 -2 4 ,x= 8 -9 6
5. Determine the courdinate vector of V =(8,-4,-12) velative to the basis S = {C,,1),(1,s,-3), (2,2,113
1. Vectors v1 = (1,1,1,1,0), v2 = (-1,1,0,0,0), v3 = (1,1,-1,-1,0), v4 = (0,0,2,-2,0) and v5 = (0,0,0,0,2) form an orthogonal basis for a of R5 and X = (-3, -2,5,1,-4). Find the coordinates of X with respect to the given basis.
Find the representation of (-5, 5, 1) in each of the following ordered bases. Your answers should be vectors of the general form . a. Represent the vector (-5, 5, 1) in terms of the ordered basis B = {ï,j,k}. [(-5, 5, 1)]B= b. Represent the vector (-5,5, 1) in terms of the ordered basis C = (ē3, ē1, ë2). [(-5, 5, 1)]c = c. Represent the vector (-5, 5, 1) in terms of the ordered basis D = {-2, -ē1, ē3}. [(-5, 5, 1)]D=
: 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

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{[i :]:[ 1 0 0 0 ; :]:[: :)-[: :]} 1 1 1 0 1 1 - Let B a basis for M2(R). = 0 0 1 1 Find the coordinate vector [A]B_ relative to the basis B, where a b (a) A (а) А — с d -1 3 (b) А — 2 5