n+m Let a1, a2,.., ,ak e R, let b1 , b2, ... , bk E R,...
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n+m Let a1, a2,.., ,ak e R", let b1 , b2, ... , bk E R", and let c1, C2, ... , Cz E R" be defined by C; = for each i = 1,2, ... , k. bị (a) If a1, a2, ak is linearly independent, and we make no assumptions about b1, b2, ... , b, does it Cg is linearly independent? Why or why not? follow C1, C2, ... , (b) If a1 , a2, follow C1, C2, az is linearly dependent, and we make no assumptions about b1, b2, ... , bk , does it Ck is linearly dependent? Why or why not? n+m Let a1, a2,.., ,ak e R", let b1 , b2, ... , bk E R", and let c1, C2, ... , Cz E R" be defined by C; = for each i = 1,2, ... , k. bị (a) If a1, a2, ak is linearly independent, and we make no assumptions about b1, b2, ... , b, does it Cg is linearly independent? Why or why not? follow C1, C2, ... , (b) If a1 , a2, follow C1, C2, az is linearly dependent, and we make no assumptions about b1, b2, ... , bk , does it Ck is linearly dependent? Why or why not?
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Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
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