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Consider the following two systems of equations: 5x1 + x2 – 3x3 — Зхз — 0 5х1 + X2 — Зхз — - 3x3 -9x1 + 2x2 + 5x3 = 1 -9x1 + 2x2 + 5x3 = 5 4x1 + x2 – 6x3 = 9 4.x1 + x2 – 6x3 = 45 = 45 It can be shown that the first system has a solution. Use this fact and the theory from this section to explain why the second system must also have a solution. (Make no row operations.)

Consider the following two systems of equations: 5x1 + x2 – 3x3 — Зхз — 0 5х1 + X2 — Зхз — - 3x3 -9x1 + 2x2 + 5x3 = 1 -9x1 + 2x2 + 5x3 = 5 4x1 + x2 – 6x3 = 9 4.x1 + x2 – 6x3 = 45 = 45 It can be shown that the first system has a solution. Use this fact and the theory from this section to explain why the second system must also have a solution. (Make no row operations.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3AEXP
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Consider the following two systems of equations: 5x1 + x2 – 3x3 — Зхз — 0 5х1 + X2 — Зхз — - 3x3 -9x1 + 2x2 + 5x3 = 1 -9x1 + 2x2 + 5x3 = 5 4x1 + x2 – 6x3 = 9 4.x1 + x2 – 6x3 = 45 = 45 It can be shown that the first system has a solution. Use this fact and the theory from this section to explain why the second system must also have a solution. (Make no row operations.)
Transcribed Image Text:Consider the following two systems of equations: 5x1 + x2 – 3x3 — Зхз — 0 5х1 + X2 — Зхз — - 3x3 -9x1 + 2x2 + 5x3 = 1 -9x1 + 2x2 + 5x3 = 5 4x1 + x2 – 6x3 = 9 4.x1 + x2 – 6x3 = 45 = 45 It can be shown that the first system has a solution. Use this fact and the theory from this section to explain why the second system must also have a solution. (Make no row operations.)
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