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your answers. 5 -3 -6 1. [ 1 7 _3]

your answers. 5 -3 -6 1. [ 1 7 _3]

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section: Chapter Questions
Problem 1RQ
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ix for e, the fying if b is in Chus A is s a linear T from ndent (by rem, and or ill- me of oduce error are 2.3 EXERCISES Unless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1-10 are invertible. Use as few calculations as possible. Justify your answers, 1. 3. 5. 400 7. 5 -3 -6 5 -3 -7 8 0 1 -4 obwt -1 -3 5 -6 -1 3 -2 Mit d 9. [M] te 075 10. [M] 3-5 0 -9 4 -6 - 5 6 7 9 8 0 1 7 -5 2 -1 OOT ST -1 34565 2 7 Oon 8 -3 3 2 2 1 23 2. 4 2 1 7 2 8 4. 1001 6. 8. -7 -7 11 9 10 19 3 -1 -7 6 1 0 -3 9 1-8 9 10 -9 -5 11 4 3 2 1 0 0 0 -9 0 0 0 536 -1 9 -4 4 0 4 6 81 3 7 5 9 0 2 0 0 10 In Exercises 11 and 12, the matrices are all n xn. Each part of the exercises is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. An implication is False if there is an instance in which "statement 2" is false but "statement 1" is true. Justify each 2.3 Cha than d. If the line then A ha e. If there inconsist to-one. 13. An m xn below the r is a square answer. 14. An mx n above the is a square answer. 15. Can a squ ible? Why 16. Is it poss columns 17. If A is L independ 18. If C is 6 v in R6, has more 19. If the co what ca 20. If nxn then E 21. If the e y in R" 22. If the e can yo 23. If an m you sa
Transcribed Image Text:ix for e, the fying if b is in Chus A is s a linear T from ndent (by rem, and or ill- me of oduce error are 2.3 EXERCISES Unless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1-10 are invertible. Use as few calculations as possible. Justify your answers, 1. 3. 5. 400 7. 5 -3 -6 5 -3 -7 8 0 1 -4 obwt -1 -3 5 -6 -1 3 -2 Mit d 9. [M] te 075 10. [M] 3-5 0 -9 4 -6 - 5 6 7 9 8 0 1 7 -5 2 -1 OOT ST -1 34565 2 7 Oon 8 -3 3 2 2 1 23 2. 4 2 1 7 2 8 4. 1001 6. 8. -7 -7 11 9 10 19 3 -1 -7 6 1 0 -3 9 1-8 9 10 -9 -5 11 4 3 2 1 0 0 0 -9 0 0 0 536 -1 9 -4 4 0 4 6 81 3 7 5 9 0 2 0 0 10 In Exercises 11 and 12, the matrices are all n xn. Each part of the exercises is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. An implication is False if there is an instance in which "statement 2" is false but "statement 1" is true. Justify each 2.3 Cha than d. If the line then A ha e. If there inconsist to-one. 13. An m xn below the r is a square answer. 14. An mx n above the is a square answer. 15. Can a squ ible? Why 16. Is it poss columns 17. If A is L independ 18. If C is 6 v in R6, has more 19. If the co what ca 20. If nxn then E 21. If the e y in R" 22. If the e can yo 23. If an m you sa
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