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Back to Gaussian elimination revisited

Exercise 9

Avg difficulty 2.5

Please provide a justification to your responses to these questions.

  1. In this section, our hypothetical computer could only store numbers using 3 decimal places. Most computers can store numbers using 15 or more decimal places. Why do we still need to be concerned about the accuracy of our computations when solving systems of linear equations?

  2. Finding the LULU factorization of a matrix AA is roughly the same amount of work as finding its reduced row echelon form. Why is the LULU factorization useful then?

  3. How can we detect whether a matrix is invertible from its LULU factorization?

Austin, Understanding Linear Algebra, §5.1 Gaussian elimination revisited, Exercise 9

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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.