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Which of the statements above are true? (Submit the corresponding number without parentheses.)  thank you <3

Which of the statements above are true? (Submit the corresponding number without parentheses.)  thank you <3

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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Which of the statements above are true?
(Submit the corresponding number without parentheses.) 

thank you <3

3 a) If A and B are invertible n x n matrices, then so is A +B. b) The rank of a 4 x 5 matrix may be 5. c) The rank of a 5 x 4 matrix may be 5. d) If S and A are invertible, then (S-'AS)-1 = S-'A-1S. e) If A and B are given n × n matrices, then there is a unique n x n matrix X satisfying (A + X)B = A if B invertible. f) It is possible that a system Ax = b has a unique solution for some b if A is a 4 x 5 matrix. g) If A is a 5 × 5 matrix such that the system Ax = 0 has only the trivial solution, then the system Ax = b is consistent for every b e R°. h) An n × n matrix of rank n is invertible. i) The system Ax = 0 has only the trivial solution if and only if there are no free variables. j) For any two n × n matrices A and B, (A +B)² = A² + 2AB+ B². k) For a 4 x 4 matrix A, det(3A)=3det(A). Which of the statements above are true? (Submit the corresponding number without parentheses.) (1) b, с, d, f, g. (2) а, b, d, i, k. (3) а, с, d, e, h. (4) d, e, g, h, i. (5) Ь, с, d, g, h, j. (6) а, с, d, f, g, k. (7) а, b, d, h, ј, k. (8) а, b, с, е, g, h, k. (9) а, с, d, e, h, i, j. (10) Ь, d, e, f, h, ј, k.
Transcribed Image Text:3 a) If A and B are invertible n x n matrices, then so is A +B. b) The rank of a 4 x 5 matrix may be 5. c) The rank of a 5 x 4 matrix may be 5. d) If S and A are invertible, then (S-'AS)-1 = S-'A-1S. e) If A and B are given n × n matrices, then there is a unique n x n matrix X satisfying (A + X)B = A if B invertible. f) It is possible that a system Ax = b has a unique solution for some b if A is a 4 x 5 matrix. g) If A is a 5 × 5 matrix such that the system Ax = 0 has only the trivial solution, then the system Ax = b is consistent for every b e R°. h) An n × n matrix of rank n is invertible. i) The system Ax = 0 has only the trivial solution if and only if there are no free variables. j) For any two n × n matrices A and B, (A +B)² = A² + 2AB+ B². k) For a 4 x 4 matrix A, det(3A)=3det(A). Which of the statements above are true? (Submit the corresponding number without parentheses.) (1) b, с, d, f, g. (2) а, b, d, i, k. (3) а, с, d, e, h. (4) d, e, g, h, i. (5) Ь, с, d, g, h, j. (6) а, с, d, f, g, k. (7) а, b, d, h, ј, k. (8) а, b, с, е, g, h, k. (9) а, с, d, e, h, i, j. (10) Ь, d, e, f, h, ј, k.
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