Which of these statements are true? a) If A and B are invertible n × n matrices, then so is A + B.b) The rank of a 4 × 5 matrixc) The rank of a 5 x 4 matrixd) If S and A are invertible, then (S-'AS)-1 = S-'A¬!s.maybe 5.maybe 5.

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a) If A and B are invertible n x 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.

a) If A and B are invertible n x 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.

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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Question

Which of these statements 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
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.

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