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Suppose that the linear system an+a12x2 + a211 + a22x2 + + ann + a₂nIn C₁ C₂ Ck akıx1+ak2k +...+ akn In has a solution X₂ = (₁, ..., æn) for each c₂ = (C₁, C₂, ..., C) in {c₁,..., cn}. Prove that the linear system has a solution x for each c in Span(c₁,..., C₂).

Suppose that the linear system an+a12x2 + a211 + a22x2 + + ann + a₂nIn C₁ C₂ Ck akıx1+ak2k +...+ akn In has a solution X₂ = (₁, ..., æn) for each c₂ = (C₁, C₂, ..., C) in {c₁,..., cn}. Prove that the linear system has a solution x for each c in Span(c₁,..., C₂).

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 an+a122 + a21x1 + a22x2 + - has a solution xi (₁,...,xn) for each c a solution x for each c in Span(c₁,..., C₂). akıx1+ak2k +...+ aknan = + ann + a2nxn (C₁, C2,.. CL C₂ Ck 2,..., Ck) in {c₁,..., Cn}. Prove that the linear system has
Transcribed Image Text:Suppose that the linear system an+a122 + a21x1 + a22x2 + - has a solution xi (₁,...,xn) for each c a solution x for each c in Span(c₁,..., C₂). akıx1+ak2k +...+ aknan = + ann + a2nxn (C₁, C2,.. CL C₂ Ck 2,..., Ck) in {c₁,..., Cn}. Prove that the linear system has
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