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Is it true that, if k > n and B is full rank, then rank AB (ii) = rank A? Justify your answer.

Is it true that, if k > n and B is full rank, then rank AB (ii) = rank A? Justify your answer.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Pls only solve for b, for b(ii), if it is false, pls give a counter example.

x +1 1 1 1 х — 2 -3 -3 (a) Let D = - 2 x + 1 - 2 1, 2, 3, 4. - x 1 Find all values of x such that rank D: (b) Let A and B be m x n and n x k matrices respectively. (i) Show that, if m > n and A is full rank, then rank AB rank B. Is it true that, if k > n and B is full rank, then rank AB (ii) = rank A? Justify your answer.
Transcribed Image Text:x +1 1 1 1 х — 2 -3 -3 (a) Let D = - 2 x + 1 - 2 1, 2, 3, 4. - x 1 Find all values of x such that rank D: (b) Let A and B be m x n and n x k matrices respectively. (i) Show that, if m > n and A is full rank, then rank AB rank B. Is it true that, if k > n and B is full rank, then rank AB (ii) = rank A? Justify your answer.
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