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Unformatted text preview: Be sure to explain your work in the diary ﬁle in addition to including all MATLAB commands and output. (a) Determine if the set S = ±² 1 2 3 4 5 6 ³ , ²2 8 4 6 91 ³ , ² 4 12 03 ³ , ² 83 2 1 10 ³ , ² 14541298 ³ , ² 12 10 12 12 20 18 ³´ forms a basis for M 23 . (b) Determine if p ( x ) =23 x2 x 2 + 7 x 3 belongs to the span of S = { p 1 ,p 2 ,p 3 ,p 4 ,p 5 } , where p 1 ( x ) = 1 + xx 2x 3 p 2 ( x ) =3x + 2 x 2 + 4 x 3x 4 p 3 ( x ) = 5 x + x 2x 4 p 4 ( x ) =1 + 3 x 3 p 5 ( x ) = 2x 2 + 2 x 4 (c) Find a basis for the nullspace of A = 2i 2 i 6 i 35 i 3 1 + i 8 i 82 i i4 + i73 ii . (d) Determine if the following subset of R 5 is linearly independent: { (0 , 8 , ,8 , 0) , (2 , , 1 ,1 , 3) , (5 ,4 , 1 , 3 , 2) , (3 , 7 , ,1 ,1) , (0 , , ,3 , 1) } . 2...
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 Winter '08
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 Linear Algebra, Algebra, matlab, Addition, Linear Independence, Vector Space, AirTrain Newark, diary file

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