Given an orthonormal basis of R³ : {V1, V2, V3} ==2-17of the following are the coefficients C₁, C₂ and C3?u=OOC₁ = 0, C₂ =C₁ =C₁ = √√C₂C1 =is expressed as a linear combination u = C₁ V₁ + C₂ V2 + C3 V3 then which one√2,02=1₁€33, C₂ =₁3-1₂ C₂ =1, C3 =√3, C3==11/613√6If11√6

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Answered: Given an orthonormal basis of R³ : {V1,…

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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Q.2) For VR2 and B = {(1,2), (3, 4)"}, C = {(7,3), (4,2)"}; consider one vector v = = (1,0) ¹. • Verity that B and C are bases for V. • Calculate [v] and [v]c. • Find two change-of-basis matrices Pc+B and PB-C.
V has bases B 2v1 + 5v2 + bv3, W3 = v1 + v2 + 5v3. (v1, v2, V3) and B' = (w1, w2, w3). If wi vi + 2v2 + 4v3, W2 = Determine the change of basis matrices, PgB and Pg¬B'-
solve parts a and b
Show that w is in span(B). We want to solve B - (-)-~-] = W = -1 Thus C₁ = 048 2 + C₂ so set up the augmented matrix of the linear system and row-reduce to solve it: [w] B = 12 1 1 0 0 -1 and C₂ = 00 8 [3]. + Find the coordinate vector [w]B. 3 R₂-2R₁ -=1/R₂2 R₁ - R₂ R₂ + R₂ 1 1 0-2 0 -1 1 0 1 0 -1 1 0 0 1 0 0 so that
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The vectors p1(t) = 1 + t², p2(t) = −t + 3t², and p3(t) = 1+t+t2 form a basis B 2(t), p3(t)} for P₂(R). Let p(t) = 1 + 2t + 4t², find its B-coordinates [p(t)B. =
Compute the quadratic form x' Ax for A = X1 5 444 X2 -9 x3 a. x = a. x¹ Ax= b. x' Ax= C. X' Ax= 1/√√3 b. x= 7 C. X = - 1/√3 1/√√3 (Simplify your answer.) 360 643 035 (Simplify your answer.) and each of the following vectors.
4
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