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Back to Pivots and their influence on solution spaces

Exercise 3

Avg difficulty 2.5

Include an example of an appropriate matrix as you justify your responses to the following questions.

  1. Suppose a linear system having six equations and three variables is consistent. Can you guarantee that the solution is unique? Can you guarantee that there are infinitely many solutions?

  2. Suppose that a linear system having three equations and six variables is consistent. Can you guarantee that the solution is unique? Can you guarantee that there are infinitely many solutions?

  3. Suppose that a linear system is consistent and has a unique solution. What can you guarantee about the pivot positions in the augmented matrix?

Austin, Understanding Linear Algebra, §1.4 Pivots and their influence on solution spaces, Exercise 3

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Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.