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Exercise 9

Avg difficulty 2.5

Suppose that AA is a matrix and there is an invertible matrix PP such that A=P [2000−30001] P−1A = P~\left[\begin{array}{rrr} 2 & 0 & 0 \\ 0 & -3 & 0 \\ 0 & 0 & 1 \\ \end{array}\right]~P^{-1}.

  1. What can you conclude about Nul(A)\nul(A)?

  2. What can you conclude about Col(A)\col(A)?

Austin, Understanding Linear Algebra, §3.5 Subspaces, 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.