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Get Full Access to Elementary Linear Algebra With Applications - 9 Edition - Chapter 4.9 - Problem 47
Get Full Access to Elementary Linear Algebra With Applications - 9 Edition - Chapter 4.9 - Problem 47

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# What can you say about the dimension of the solution 'pal:e uf a humugeneuus syslem uf 8

ISBN: 9780132296540 301

## Solution for problem 47 Chapter 4.9

Elementary Linear Algebra with Applications | 9th Edition

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Problem 47

What can you say about the dimension of the solution 'pal:e uf a humugeneuus syslem uf 8 e4U

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M303 Section 4.3 Notes- Bases of Subspaces 11-2-16  Spanning sets give explicit description of a space, but can have redundancy o Linearly independent set will not have redundancies  As in chapter 1, nonempty se{ ,,…, } of vectors in vector space is linearly independent if only solution to 1 + 2 + ⋯+ is trivial solution (all = 0) o Otherwise, set linearly dependent; dependence relation on the occurs when at least one ≠ 0 o For any , set linearly dependent iff = ; ,}linearly dependent if1 = 2 ; any set containing zero vector automatically linearly dependent { }  Ex. Let = ℙ2, = 1, = , 4 − . Is the set ,, linearly independent o Dependent, because we can write = 4 − , hich gives − − =  Ex. The set cos,sin ⊆ ℝ is linearly independent o Not scalar multiples o Suppose cos = sin for some scalar  cos0 = sin0  1 = 0)  1 ≠ 0 o Not possible to create dependence relation  Let be subspace of

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