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Mathematics LibreTexts

3: Invertibility, bases, and coordinate systems

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In Chapter 2, we examined our two fundamental questions, Question 1.4.2, concerning the existence and uniqueness of solutions to linear systems independently of one another. We found that every equation of the form Ax=b has a solution when the columns of A span .Rm. We also found that any solution of the equation Ax=b is unique when the columns of A are linearly independent. In this chapter, we explore the situation in which these two conditions hold simultaneously.


This page titled 3: Invertibility, bases, and coordinate systems is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by David Austin via source content that was edited to the style and standards of the LibreTexts platform.

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