Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Exercise Set 1.3 In Exercises 1-2, suppose that A, B, C, D, and E are matrices with the following sizes: A B с D E (4 x 5) (4x5) (5x2) (4x2) (5x4) In each part, determine whether the given matrix expression is defined. For those that are defined, give the size of the resulting matrix. 1. a. BA b. ABT c. AC + D f F(SB d F(AC) RET

Exercise Set 1.3 In Exercises 1-2, suppose that A, B, C, D, and E are matrices with the following sizes: A B с D E (4 x 5) (4x5) (5x2) (4x2) (5x4) In each part, determine whether the given matrix expression is defined. For those that are defined, give the size of the resulting matrix. 1. a. BA b. ABT c. AC + D f F(SB d F(AC) RET

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 21T
See similar textbooks
icon
Related questions
Question
Exercise Set 1.3 In Exercises 1-2, suppose that A, B, C, D, and E are matrices with the following sizes: A B с D (4x2) E (5x4) (4 x 5) (4 x 5) (5 x 2) In each part, determine whether the given matrix expression is defined. For those that are defined, give the size of the resulting matrix. 1. a. BA b. ABT c. AC + D d. E(AC) e. A - 3ET f. E(5B + A) 6. 2. a. CDT b. DC c. BC - 3D d. DT (BE) e. BTD + ED f. BAT + D In Exercises 3-6, use the following matrices to compute the indicated expression if it is defined. 3 4 4 2 A = = 6 -1 c = ₁3₂ 13³ 1 2 6 1 31 D = 0 1 1 2 2 4 4 1 3 b. D - E c. 5A e. 2B - C f. 4E-2D h. A - A i. tr(D) k. 4 tr(7B) 1. tr(A) b. DT - ET c. (D-E)T e. CT - A f. B - BT 3. a. D+E d. -7C g. -3(D+2E) j. tr(D-3E) a. 2AT + C d. BT + 5CT 4. -1 3 B = 1 5 E = -1 h. (2ET-3DT)T i. (CD)E k. tr(DET) 1. tr(BC) b. BA c. (3E)D d. (AB)C e. A(BC) f. CCT g. (DA)T h. (CTB)AT i. tr(DDT) j. tr(4E¹-D) k. tr(CTAT +2ET) 1. tr((ECT)¹A) a. (2D¹ - E)A b. (4B)C + 2B c. (-AC)¹ + 5D" d. (BAT - 2C)T e. B¹(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. -2 7 6 -2 4 3 A = 6 5 4 and B = 0 1 3 0 4 9 [7 7 5 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 8. a. the first column of AB b. the third column of BB d. the first column of AA c. the second row of BB 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. g. 2ET-3DT j. C(BA) 5. a. AB
Transcribed Image Text:Exercise Set 1.3 In Exercises 1-2, suppose that A, B, C, D, and E are matrices with the following sizes: A B с D (4x2) E (5x4) (4 x 5) (4 x 5) (5 x 2) In each part, determine whether the given matrix expression is defined. For those that are defined, give the size of the resulting matrix. 1. a. BA b. ABT c. AC + D d. E(AC) e. A - 3ET f. E(5B + A) 6. 2. a. CDT b. DC c. BC - 3D d. DT (BE) e. BTD + ED f. BAT + D In Exercises 3-6, use the following matrices to compute the indicated expression if it is defined. 3 4 4 2 A = = 6 -1 c = ₁3₂ 13³ 1 2 6 1 31 D = 0 1 1 2 2 4 4 1 3 b. D - E c. 5A e. 2B - C f. 4E-2D h. A - A i. tr(D) k. 4 tr(7B) 1. tr(A) b. DT - ET c. (D-E)T e. CT - A f. B - BT 3. a. D+E d. -7C g. -3(D+2E) j. tr(D-3E) a. 2AT + C d. BT + 5CT 4. -1 3 B = 1 5 E = -1 h. (2ET-3DT)T i. (CD)E k. tr(DET) 1. tr(BC) b. BA c. (3E)D d. (AB)C e. A(BC) f. CCT g. (DA)T h. (CTB)AT i. tr(DDT) j. tr(4E¹-D) k. tr(CTAT +2ET) 1. tr((ECT)¹A) a. (2D¹ - E)A b. (4B)C + 2B c. (-AC)¹ + 5D" d. (BAT - 2C)T e. B¹(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. -2 7 6 -2 4 3 A = 6 5 4 and B = 0 1 3 0 4 9 [7 7 5 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 8. a. the first column of AB b. the third column of BB d. the first column of AA c. the second row of BB 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. g. 2ET-3DT j. C(BA) 5. a. AB
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS