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In Excrcises 34-37, solve the given linear system and express the solution set in a form that illustrates Theorem 1.18. - 34. x₁ − 2x2 + x3 + 5x₁ = 7

In Excrcises 34-37, solve the given linear system and express the solution set in a form that illustrates Theorem 1.18. - 34. x₁ − 2x2 + x3 + 5x₁ = 7

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.5: Cramer's Rule
Problem 35PS
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THEOREM 1.18 Structure of the Solution Set of Ax = b Let Ax = b be a linear system. If p is any particular solution of Ax = b and h is a solution of the corresponding homogeneous system Ax = 0, then p + h is a solution of Ax = b. Moreover, every solution of Ax = b has this form p + h, so that the general solution is x = p + h where Ah = 0.
Transcribed Image Text:THEOREM 1.18 Structure of the Solution Set of Ax = b Let Ax = b be a linear system. If p is any particular solution of Ax = b and h is a solution of the corresponding homogeneous system Ax = 0, then p + h is a solution of Ax = b. Moreover, every solution of Ax = b has this form p + h, so that the general solution is x = p + h where Ah = 0.
In Excrcises 34-37, solve the given linear system and express the solution set in a form that illustrates Theorem 1.18. - 34. x₁ − 2x2 + x3 + 5x4 = 7 - 35. 2x, x₂+ 3×3 4x + 2x2 = -3 - X₁ = |
Transcribed Image Text:In Excrcises 34-37, solve the given linear system and express the solution set in a form that illustrates Theorem 1.18. - 34. x₁ − 2x2 + x3 + 5x4 = 7 - 35. 2x, x₂+ 3×3 4x + 2x2 = -3 - X₁ = |
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