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Exercise 5.5.3

Avg difficulty 3.0

In this exercise, we use scalars from the field Z5\mathbb{Z}_{5} of integers modulo 55 instead of real numbers (see Section an exercise given elsewhere in the book, “Fields”). Determine the rank and nullity and find a basis of the column space, row space, and null space of the following matrix over Z5\mathbb{Z}_{5}.

A=[241123312]A=\left[\begin{array}{rrr}2&4&1\\ 1&2&3\\ 3&1&2\\ \end{array}\right]

Selinger, Matrix Theory and Linear Algebra, Spans, linear independence, and bases in Rn, Column space, row space, and null space of a matrix, Exercise 5.5.3

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.