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Exercise 28

Avg difficulty 3.0

What is the relationship between rank⁡(A)\operatorname{rank}(A) and rank⁡(−A)\operatorname{rank}(-A)? Between rank⁡(A)\operatorname{rank}(A) and rank⁡(kA)\operatorname{rank}(kA)? What, if any, is the relationship between rank⁡(A)\operatorname{rank}(A), rank⁡(B)\operatorname{rank}(B), and rank⁡(A+B)\operatorname{rank}(A+B)?

Hefferon, Linear Algebra, Vector Spaces, Vector Spaces and Linear Systems, Exercise 28

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.