# nov1109 - Math 1502 D November 11th 2009 1 School of...

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Unformatted text preview: Math 1502 D, November 11th 2009 1 School of Mathematics Math 1502 D Georgia Tech Calculus II Quiz # 10 November 11th 2009 15 minutes First Name : Last Name : −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− 110 1. Let A = −1 1 2 . 2 −1 −3 (a) Give a basis for Im(A) (Give results here and use the back pages for your calculations) (b) Give a basis for Ker(A) (Give results here and use the back pages for your calculations) Math 1502 D, November 11th 2009 2 2. Let S be the set of x ∈ R4 such that x1 +3x2 −2x3 = 0 and x2 −4x4 = 0. (a) Show that S is a linear space (b) Give the dimension of S (Give results here and use the back pages for your calculations) dim(S ) = Math 1502 D, November 11th 2009 3 1 1 0 −1 3. Let v1 = , v2 = 1 1 0 −1 independent ? 0 and v3 = 1 . Are they linearly 0 1 YES 2 NO 2 Justiﬁcation : −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− Use the bottom of this page and the back pages for your calculations Math 1502 D, November 11th 2009 4 Use this page for your calculations ...
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## This note was uploaded on 11/30/2009 for the course MATH 1502 taught by Professor Mcclain during the Fall '07 term at Georgia Tech.

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