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A system of equations is called homogeneous if the right-hand-sides of each equation is 0. So it looks something like this: ₁x₁ + ₁x2 +₁x3+d₁x₁ = 0 a2x1 + b2x2 +c₂x3 + d₂x4 = 0 a3x1 + b3x2 +C3x3 +d3x4=0 a4x1b4x2 +C4x3 + d4x4 =0 Eva looks at this and says she knows what will always be a solution to a homogeneous system of equations. What is it and why?

A system of equations is called homogeneous if the right-hand-sides of each equation is 0. So it looks something like this: ₁x₁ + ₁x2 +₁x3+d₁x₁ = 0 a2x1 + b2x2 +c₂x3 + d₂x4 = 0 a3x1 + b3x2 +C3x3 +d3x4=0 a4x1b4x2 +C4x3 + d4x4 =0 Eva looks at this and says she knows what will always be a solution to a homogeneous system of equations. What is it and why?

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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A system of equations is called homogeneous if the right-hand-sides of each equation is 0. So it looks something like this: ₁x₁ + ₁x2 +₁x3+d₁x₁ = 0 a2x1 + b2x2 +c₂x3+d₂x4 = 0 a3x1 + b3x2 +C3x3 + d3x4 = 0 a4x₁ + b4x2 +C4x3 +d4x4 = 0 Eva looks at this and says she knows what will always be a solution to a homogeneous system of equations. What is it and why?
Transcribed Image Text:A system of equations is called homogeneous if the right-hand-sides of each equation is 0. So it looks something like this: ₁x₁ + ₁x2 +₁x3+d₁x₁ = 0 a2x1 + b2x2 +c₂x3+d₂x4 = 0 a3x1 + b3x2 +C3x3 + d3x4 = 0 a4x₁ + b4x2 +C4x3 +d4x4 = 0 Eva looks at this and says she knows what will always be a solution to a homogeneous system of equations. What is it and why?
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