is an invertible matrix. A is row equivalent to the n x n identity matrix. A has n pivot positions. The equation Ax=0 has only the trivial solution. The columns of A form a linearly independent set. The linear transformation x Ax is one-to-one. The equation Ax=b has at least one solution for each b € Rn. The columns of A span R". The linear transformation x→ Ax maps R" onto R". There is an n x n matrix C such that CA = I. There is an n x n matrix D such that AD = I. AT is an invertible matrix.

is an invertible matrix. A is row equivalent to the n x n identity matrix. A has n pivot positions. The equation Ax=0 has only the trivial solution. The columns of A form a linearly independent set. The linear transformation x Ax is one-to-one. The equation Ax=b has at least one solution for each b € Rn. The columns of A span R". The linear transformation x→ Ax maps R" onto R". There is an n x n matrix C such that CA = I. There is an n x n matrix D such that AD = I. AT is an invertible matrix.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 23EQ

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