Which of the following statements are always true? (i) Suppose that A and B are n×n matrices. If the matrix AB is invertible then B can be expressed as a product of elementary matrices. (ii) If A and B are invertible matrices then then (BA)x 0 has only the trivial solution. (iii) If A is an invertible 38 x 38 matrix then the reduced row-echelon form of A' is the identity matrix.

Which of the following statements are always true? (i) Suppose that A and B are n×n matrices. If the matrix AB is invertible then B can be expressed as a product of elementary matrices. (ii) If A and B are invertible matrices then then (BA)x 0 has only the trivial solution. (iii) If A is an invertible 38 x 38 matrix then the reduced row-echelon form of A' is the identity matrix.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.1: Operations With Matrices

Problem 77E

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In general, it is difficult to show that two matrices are similar. However, if two similar matrices are diagonalizable, the task becomes easier. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. Then find an invertible matrix P such that .
11. Find two nonzero matrices and such that.
True or false? det(A) is defined only for a square matrix A.

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