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Exercise 6

Avg difficulty 2.5

This exercise asks you to construct some matrices whose columns span a given set.

  1. Construct a 3×33\times3 matrix whose columns span R3\real^3.

  2. Construct a 3×33\times3 matrix whose columns span a plane in R3\real^3.

  3. Construct a 3×33\times3 matrix whose columns span a line in R3\real^3.

Austin, Understanding Linear Algebra, §2.3 The span of a set of vectors, Exercise 6

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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.