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13. 14 x₁ + 3x₂ = b₁ -2x₁ + x₂ = b₂ : 15. x₁2x₂ + 5x3 = b₁ 16 4x₁5x₂ + 8x3 = b₂ -3x₂ + 3x₂ - 3x3 = b3 17. X₁ X₂ + 3x3 + 2x₁ = b₁ -

13. 14 x₁ + 3x₂ = b₁ -2x₁ + x₂ = b₂ : 15. x₁2x₂ + 5x3 = b₁ 16 4x₁5x₂ + 8x3 = b₂ -3x₂ + 3x₂ - 3x3 = b3 17. X₁ X₂ + 3x3 + 2x₁ = b₁ -

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1.6 Questions 15 on paper please
11. 4x₁7x₂ = b₁ x₁ + 2x₂ = b₂ i. b, = 0, iii. b₁ = -1, b₂ = 1 b₂ = 3 ii. b, = -4, b₂ = 6 iv. b, = -5, b₂ = 1 x₁ + 3x₂ + 5x3 = b₁ -x₁ - 2x₂ =b₂ 2x₁ + 5x₂ + 4x3 = bz i. b₁ = 1, b₂ = 0, b₂ = -1 ii. b₁ = 0, b₂ = 1, b₂ = 1 iii. b, = -1, b₂ = -1, b3 = 0 In Exercises 13-17, determine conditions on the b's, if any, in order to guarantee that the linear system is consistent. 13. x₁ + 3x₂ = b₁ 14. 6x₁4x₂ = b₁ 3x₁2x₂ = b₂ -2x₁ + x₂ = b₂ 15. 16. x₁2x₂ + 5x3 = b₁ 4x₁5x₂ + 8x3 = b₂ X₁2x₂x3 = b₁ -4x₁ + 5x₂ + 2x3 = b₂ -4x₁ + 7x₂ + 4x3 = b₂ -3x₂ + 3x₂ 3x3 = b3 17. X₁ -2x₁ + x₂ + 5x3 + -3x₁ + 2x₂ + 2x3 = X₂ + 3x3 + 2x4 = b₁ x4 = b₂2 x₁ = b3 4x₁3x₂ + x3 + 3x4=b4 18. Consider the matrices [2 1 27 X1 A = 2 2 -2 and x = x₂ 3 1 1 X3 a. Show that the equation Ax= x can be rewritten as (A-I)x= 0 and use this result to solve Ax = x for x. b. Solve Ax = 4x. In Exercises 19-20, solve the matrix equation for X. 1 -1 2 -1 5 7 8 19. 2 3 0 X = 4 0 -3 0 1 0 2 -1 5 -7 2 1 -2 0 [4 3 20. 0 -1 -1 X = 6 7 1 1 -4 Working with Proofs 12. 43 tem can be written in tion to Ax= 0. Pro solution. 24. Use part (a) of The True-False Exercis TF. In parts (a)-(g) false, and justify a. It is impossi exactly two b. If A is a sq has a uniqu must have c. If A and 1 BA=In. d. If A and systems A e. Let A b matrix. then Sx f. Let A br a uniqu matrix 2 1 89 [1 3 7 9 g. Let A invert Working wi T1. Colors in vision sc models." mixing the YIC by mixi of a chr conver plished
Transcribed Image Text:11. 4x₁7x₂ = b₁ x₁ + 2x₂ = b₂ i. b, = 0, iii. b₁ = -1, b₂ = 1 b₂ = 3 ii. b, = -4, b₂ = 6 iv. b, = -5, b₂ = 1 x₁ + 3x₂ + 5x3 = b₁ -x₁ - 2x₂ =b₂ 2x₁ + 5x₂ + 4x3 = bz i. b₁ = 1, b₂ = 0, b₂ = -1 ii. b₁ = 0, b₂ = 1, b₂ = 1 iii. b, = -1, b₂ = -1, b3 = 0 In Exercises 13-17, determine conditions on the b's, if any, in order to guarantee that the linear system is consistent. 13. x₁ + 3x₂ = b₁ 14. 6x₁4x₂ = b₁ 3x₁2x₂ = b₂ -2x₁ + x₂ = b₂ 15. 16. x₁2x₂ + 5x3 = b₁ 4x₁5x₂ + 8x3 = b₂ X₁2x₂x3 = b₁ -4x₁ + 5x₂ + 2x3 = b₂ -4x₁ + 7x₂ + 4x3 = b₂ -3x₂ + 3x₂ 3x3 = b3 17. X₁ -2x₁ + x₂ + 5x3 + -3x₁ + 2x₂ + 2x3 = X₂ + 3x3 + 2x4 = b₁ x4 = b₂2 x₁ = b3 4x₁3x₂ + x3 + 3x4=b4 18. Consider the matrices [2 1 27 X1 A = 2 2 -2 and x = x₂ 3 1 1 X3 a. Show that the equation Ax= x can be rewritten as (A-I)x= 0 and use this result to solve Ax = x for x. b. Solve Ax = 4x. In Exercises 19-20, solve the matrix equation for X. 1 -1 2 -1 5 7 8 19. 2 3 0 X = 4 0 -3 0 1 0 2 -1 5 -7 2 1 -2 0 [4 3 20. 0 -1 -1 X = 6 7 1 1 -4 Working with Proofs 12. 43 tem can be written in tion to Ax= 0. Pro solution. 24. Use part (a) of The True-False Exercis TF. In parts (a)-(g) false, and justify a. It is impossi exactly two b. If A is a sq has a uniqu must have c. If A and 1 BA=In. d. If A and systems A e. Let A b matrix. then Sx f. Let A br a uniqu matrix 2 1 89 [1 3 7 9 g. Let A invert Working wi T1. Colors in vision sc models." mixing the YIC by mixi of a chr conver plished
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