a) If A and B are invertible n × n matrices, then so is A + B. b) The rank of a 4 × 5 matrix c) The rank of a 5 x 4 matrix d) If S and A are invertible, then (S-'AS)-1 = S-'A¬!s. may be 5. may be 5.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
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Which of the statements above are true?

a) If A and B are invertible n × n matrices, then so is A +B.
b) The rank of a 4 × 5 matrix may be 5.
c) The rank of a 5 × 4 matrix may be 5.
d) If S and A are invertible, then (S-'AS)-1 = s-'A-1s.
Transcribed Image Text:a) If A and B are invertible n × n matrices, then so is A +B. b) The rank of a 4 × 5 matrix may be 5. c) The rank of a 5 × 4 matrix may be 5. d) If S and A are invertible, then (S-'AS)-1 = s-'A-1s.
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