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Suppose that the linear system a11x1 + a12x2 + + A1nXn a21x1 + a22x2 + ... + A 2nX n C1 = C2 ak1x₁ + ak2x2 + ... + Akn xn has a solution x₂ = (x₁,...,xn) for each c₂ = (C₁, C₂, ..., Ck) in {c1₁,..., Cn}. Prove that the linear system has a solution x for each c in Span(c₁,..., Cn). = Ck

Suppose that the linear system a11x1 + a12x2 + + A1nXn a21x1 + a22x2 + ... + A 2nX n C1 = C2 ak1x₁ + ak2x2 + ... + Akn xn has a solution x₂ = (x₁,...,xn) for each c₂ = (C₁, C₂, ..., Ck) in {c1₁,..., Cn}. Prove that the linear system has a solution x for each c in Span(c₁,..., Cn). = Ck

Advanced Engineering Mathematics
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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Suppose that the linear system a11x1 + a12x2 + ... + Ain xn a21x1 + a22x2 + ... + A2nX n akı x₁ + ak2x2 + ... + Akn x n = has a solution x₂ = (x₁,...,xn) for each ci has a solution x for each c in Span (C₁,..., Cn). = C1 C2 Ck (C₁, C₂,..., c) in {c₁,..., Cn}. Prove that the linear system
Transcribed Image Text:Suppose that the linear system a11x1 + a12x2 + ... + Ain xn a21x1 + a22x2 + ... + A2nX n akı x₁ + ak2x2 + ... + Akn x n = has a solution x₂ = (x₁,...,xn) for each ci has a solution x for each c in Span (C₁,..., Cn). = C1 C2 Ck (C₁, C₂,..., c) in {c₁,..., Cn}. Prove that the linear system
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