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Exercise 5

Avg difficulty 2.5

For each of the following conditions, construct a 3×33\times 3 matrix having the given properties.

  1. dim⁡ Nul(A)=0\dim~\nul(A) = 0.

  2. dim⁡ Nul(A)=1\dim~\nul(A) = 1.

  3. dim⁡ Nul(A)=2\dim~\nul(A) = 2.

  4. dim⁡ Nul(A)=3\dim~\nul(A) = 3.

Austin, Understanding Linear Algebra, §3.5 Subspaces, Exercise 5

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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.