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x₁ - 5x₂ = ₁ X1 3x₁ + 2x₂ = b₂ i. b₁ = 1, b₂ = 4 ii. b₁ = -2, b₂ = 5

x₁ - 5x₂ = ₁ X1 3x₁ + 2x₂ = b₂ i. b₁ = 1, b₂ = 4 ii. b₁ = -2, b₂ = 5

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 94E
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1.6 Question 9 and 15 please on paper. Thanks alot
1. b₁ = 1, b₂ = 0, b₂ ii. b₁ = 0, b₂ = 1, b₂ = 1 iii. b₁ = -1, b₂ = -1, b₂ = 0 In Exercises 13-17, determine conditions on the bi's, if any, in order to guarantee that the linear system is consistent. 13. 14. 6x₁4x₂ = b₁ x₁ + 3x₂ = b₁ -2x₁ + x₂ = b₂ 3x₁ - 2x₂ = b₂ 15. 16. X₁ - 2x₂ + 5x3 = b₁ 4x₁ - 5x₂ + 8x3 = b₂ -3x₁ + 3x₂ - 3x3 = b3 x₁2x₂x3 = b₁ -4x₁ + 5x₂ + 2x3 = b₂ -4x₁ + 7x₂ + 4x3 = b3 x₁ - x₂ + 3x3 + 2x₁ = b₁ -2x₁ + x₂ + 5x3 + x₁ = b₂ X2 X4 -3x₁ + 2x₂ + 2x3 x4 = b3 4x13x₂ + x3 + 3x4 = b4 17. 18. Consider the matrices
Transcribed Image Text:1. b₁ = 1, b₂ = 0, b₂ ii. b₁ = 0, b₂ = 1, b₂ = 1 iii. b₁ = -1, b₂ = -1, b₂ = 0 In Exercises 13-17, determine conditions on the bi's, if any, in order to guarantee that the linear system is consistent. 13. 14. 6x₁4x₂ = b₁ x₁ + 3x₂ = b₁ -2x₁ + x₂ = b₂ 3x₁ - 2x₂ = b₂ 15. 16. X₁ - 2x₂ + 5x3 = b₁ 4x₁ - 5x₂ + 8x3 = b₂ -3x₁ + 3x₂ - 3x3 = b3 x₁2x₂x3 = b₁ -4x₁ + 5x₂ + 2x3 = b₂ -4x₁ + 7x₂ + 4x3 = b3 x₁ - x₂ + 3x3 + 2x₁ = b₁ -2x₁ + x₂ + 5x3 + x₁ = b₂ X2 X4 -3x₁ + 2x₂ + 2x3 x4 = b3 4x13x₂ + x3 + 3x4 = b4 17. 18. Consider the matrices
8. 7. 3x₁ + 5x₂ = b₁ x₂ + 2x₂ = b₂ x₁ + 2x₂ + 3x₂, = b₁ 2x₁ + 5x₂ + 5x3 = b₂ 3x₁ + 5x₂ + 8x3 = b₂ In Exercises 9-12, solve the linear systems. Using the given values for the b's solve the systems together by reducing an appropriate aug- mented matrix to reduced row echelon form. 9. X₁ - 5x₂ = b₁ 3x₁ + 2x₂ = b₂ ii. b₁ = -2, b₂ = 5 i. b₁ = 1, b₂ = 4 x3 = b₁ x₁ + 9x₂ - 2x3 = b₂ 6x₁ + 4x₂ - 8x3 = b3 i. b₁ = 0, b₂ = 1, b3 = 0 ii. b₁ = -3, b₂ = 4, b3 = -5 10. -x₁ + 4x₂ +
Transcribed Image Text:8. 7. 3x₁ + 5x₂ = b₁ x₂ + 2x₂ = b₂ x₁ + 2x₂ + 3x₂, = b₁ 2x₁ + 5x₂ + 5x3 = b₂ 3x₁ + 5x₂ + 8x3 = b₂ In Exercises 9-12, solve the linear systems. Using the given values for the b's solve the systems together by reducing an appropriate aug- mented matrix to reduced row echelon form. 9. X₁ - 5x₂ = b₁ 3x₁ + 2x₂ = b₂ ii. b₁ = -2, b₂ = 5 i. b₁ = 1, b₂ = 4 x3 = b₁ x₁ + 9x₂ - 2x3 = b₂ 6x₁ + 4x₂ - 8x3 = b3 i. b₁ = 0, b₂ = 1, b3 = 0 ii. b₁ = -3, b₂ = 4, b3 = -5 10. -x₁ + 4x₂ +
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