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10. a. Express each column vector of AB as a linear combination of the column vectors of A. b. Express each column vector of BA as a linear combination of the column vectors of B. In each part of Exercises 11-12, find matrices A, x, and b that express the given linear system as a single matrix equation Ax = b, and write out this matrix equation. 11. a. 2x₁ - 3x₂ + 5x3 = 7 9x1 - x₂ + x3 = -1 x₁ + 5x₂ + 4x3 = 0 - 3x3 + x4 = 1 5x₁ + x₂ − 8x = 3 X4 = 0 2x1 5x2 + 9x3 3x2x3 + 7x4 = 2 b. 4x1

10. a. Express each column vector of AB as a linear combination of the column vectors of A. b. Express each column vector of BA as a linear combination of the column vectors of B. In each part of Exercises 11-12, find matrices A, x, and b that express the given linear system as a single matrix equation Ax = b, and write out this matrix equation. 11. a. 2x₁ - 3x₂ + 5x3 = 7 9x1 - x₂ + x3 = -1 x₁ + 5x₂ + 4x3 = 0 - 3x3 + x4 = 1 5x₁ + x₂ − 8x = 3 X4 = 0 2x1 5x2 + 9x3 3x2x3 + 7x4 = 2 b. 4x1

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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(1.3) Questions 10 and 11 on paper please thank you.
c. (-AC)T + 5DT d. (BAT-2C)T e. BT(CCT-ATA) f. DTET - (ED)T In Exercises 7-8, use the following matrices and either the row method or the column method, as appropriate, to find the indicated row or column. d -2 7 6 2 4 A = 6 5 4 and B = 0 1 3 0 4 7 7. a. the first row of AB b. the third row of AB c. the second column of AB d. the first column of BA e. the third row of AA f. the third column of AA a. the first column of AB b. the third column of BB c. the second row of BB d. the first column of AA e. the third column of AB f. the first row of BA In Exercises 9-10, use matrices A and B from Exercises 7-8. 9. a. Express each column vector of AA as a linear combination of the column vectors of A. b. Express each column vector of BB as a linear combination of the column vectors of B. 8.
Transcribed Image Text:c. (-AC)T + 5DT d. (BAT-2C)T e. BT(CCT-ATA) f. DTET - (ED)T In Exercises 7-8, use the following matrices and either the row method or the column method, as appropriate, to find the indicated row or column. d -2 7 6 2 4 A = 6 5 4 and B = 0 1 3 0 4 7 7. a. the first row of AB b. the third row of AB c. the second column of AB d. the first column of BA e. the third row of AA f. the third column of AA a. the first column of AB b. the third column of BB c. the second row of BB d. the first column of AA e. the third column of AB f. the first row of BA In Exercises 9-10, use matrices A and B from Exercises 7-8. 9. a. Express each column vector of AA as a linear combination of the column vectors of A. b. Express each column vector of BB as a linear combination of the column vectors of B. 8.
38 CHAPTER 1 Systems of Linear Equations and Matrices 10. a. Express each column vector of AB as a linear combination of the column vectors of A. b. Express each column vector of BA as a linear combination of the column vectors of B. In each part of Exercises 11-12, find matrices A, x, and b that express the given linear system as a single matrix equation Ax = b, and write out this matrix equation. 11. a. 2x₁ 3x₂ + 5x31 = 7 9x₁ - x₂ + x3 = -1 X₁ + 5x₂ + 4x3 = 0 - 3x3 + x₁ = = 1 5x₁ + x₂ − 8x = 3 X4 = 0 2x1 5x2 +9X3 3x₂x3 + 7x4 = 2 12. a. x₁2x2 + 3x3 = -3 b. 3x₁ + 3x₂ + 3x3 = -3 - 5x₂ - 2x3 = 3 2x₁ + x₂ = 0 -X1 - 3x₂ + 4x3 - 1 - 4x₂ + x3 = 0 X1 + x3 = 5 In each part of Exercises 13-14, express the matrix equation as a sys- tem of linear equations. 5 6 -7X₁ 13. a. -1 -2 3 X2 0 4 -1 X₂3 b. 4x₁
Transcribed Image Text:38 CHAPTER 1 Systems of Linear Equations and Matrices 10. a. Express each column vector of AB as a linear combination of the column vectors of A. b. Express each column vector of BA as a linear combination of the column vectors of B. In each part of Exercises 11-12, find matrices A, x, and b that express the given linear system as a single matrix equation Ax = b, and write out this matrix equation. 11. a. 2x₁ 3x₂ + 5x31 = 7 9x₁ - x₂ + x3 = -1 X₁ + 5x₂ + 4x3 = 0 - 3x3 + x₁ = = 1 5x₁ + x₂ − 8x = 3 X4 = 0 2x1 5x2 +9X3 3x₂x3 + 7x4 = 2 12. a. x₁2x2 + 3x3 = -3 b. 3x₁ + 3x₂ + 3x3 = -3 - 5x₂ - 2x3 = 3 2x₁ + x₂ = 0 -X1 - 3x₂ + 4x3 - 1 - 4x₂ + x3 = 0 X1 + x3 = 5 In each part of Exercises 13-14, express the matrix equation as a sys- tem of linear equations. 5 6 -7X₁ 13. a. -1 -2 3 X2 0 4 -1 X₂3 b. 4x₁
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