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Exercise 2

Avg difficulty 2.5

Suppose that A=[20−2−4−2−1120−1−1−2]A = \left[\begin{array}{rrrr} 2 & 0 & -2 & -4 \\ -2 & -1 & 1 & 2 \\ 0 & -1 & -1 & -2 \end{array}\right].

  1. Is the vector [0−1−1]\threevec{0}{-1}{-1} in Col(A)\col(A)?

  2. Is the vector [2102]\fourvec{2}{1}{0}{2} in Col(A)\col(A)?

  3. Is the vector [2−20]\threevec{2}{-2}{0} in Nul(A)\nul(A)?

  4. Is the vector [1−13−1]\fourvec{1}{-1}{3}{-1} in Nul(A)\nul(A)?

  5. Is the vector [101−1]\fourvec{1}{0}{1}{-1} in Nul(A)\nul(A)?

Austin, Understanding Linear Algebra, §3.5 Subspaces, Exercise 2

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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.