c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This]A a 5x5 real matrix & v₁,..., v5 linearly independent real vectors in 5 dimensional space:Av₁ = (-5)v₁Av₂ = (7)v₂Av₂ = (7)v₂A(v₁ +vši)=(3+2i) (v₁ +vši) 1) For the following matrices A:J₁0 0.. 0i) Write A in the form BAB¯¹, with A = 00where J, =[^] with λ real OR J=0 J₁tb[1]-bii) Describe what A is doing in the basis whose members are the columns of B:with a and b real;

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Answered: c) [For Susan Foreman of 76 Totter's…

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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as a1 Let V₁ = (3).. b₁ b₂ b4 be four vectors in R³. V3 = C1 C2 C4 a1 a2 a3 a4 If we reduce the matrix A = b₁ b₂ b3 b4 to reduced echelon form, we get the following matrix: C1 C2 C3 C4 /1 0 0 3 0 1 0 5 0 0 17, Which one of the following statements must be true? Select one alternative: © The set {V₁, V2, V3} is linearly dependent. v4 is a linear combination of V₁, V2, and V3 The set {V₁, V2, V3, V4} is linearly independent. V3 is a linear combination of v₁ and v2. V2 = a2 az b3 C3 V4 =
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c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real matrix & V₁,..., V, linearly independent real vectors in 5 dimensional space: Av₁ = (-5)v₁ Av₂ = (7)v₂ Av3 = (7)v3 A(v4 +vsi)=(3+2i) (v₁ +vsi)