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Quiz 5 - Solutions

# Quiz 5 - Solutions - 1-3-1 2 1 5 1 2 Consider the set S = t...

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Math 54 Quiz 5 Mike Hartglass November 6, 2010 1.) Consider the matrix A = 1 2 0 - 3 1 2 - 1 5 2 . Find bases for the null space and the column space of A . This matrix can be row reduced to 1 2 0 0 7 2 0 0 0 so by writing the appropriate aug- mented matrix and solving Ax = 0 we see that x 2 = - 2 x 3 / 7 and x 1 = - 2 x 2 = 4 x 3 / 7 so the null space must be one dimensional and it has a basis of 4 / 7 - 2 / 7 1 . Thus by the rank-nullity theorem, the column space must be dimension 2 so it has a basis

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Unformatted text preview: 1-3-1 , 2 1 5 1 2.) Consider the set S = { ( t + 1) 2 , (1-t ) 3 ,t-2 , 5 t 2-5 ,t 3 + 2 } . Determine if S is a basis for P 3 . Explain your answer. P 3 is a 4 dimensional vector space and the set S has 5 elements so S can not be a basis as any such basis would have to have only 4 elements. 2...
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