Practice_exam2 - MATH 3000 EXAM 2 PRACTICE SHEET Computation(1 Find a basis for Span(1 0 1 2(2 3 0 0(1 3 1 2(2 Find a basis for Span(1 0 1 2(2 3 0

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MATH 3000 EXAM 2 PRACTICE SHEET Computation (1) Find a basis for Span ± (1 , 0 , 1 , 2) , (2 , 3 , 0 , 0) , (1 , 3 , - 1 , - 2) ² (2) Find a basis for Span ± (1 , 0 , 1 , 2) , (2 , 3 , 0 , 0) , (1 , 3 , - 1 , - 2) ² (3) Consider the following system of equations: x 1 + x 3 + 2 x 4 = 0 2 x 1 + 3 x 2 = 0 x 1 + 3 x 2 - x 3 - 2 x 4 = 0 (a) Solve (write down the general solution to) the system of equations above. (b) Let V = ³ ~x = ( x 1 ,x 2 ,x 3 ,x 4 ) ´ ´ ´ ´ ~x is a solution to the system above µ . Find a basis for V . (4) Find conditions on the coordinates of the vector b = ( b 1 ,b 2 ,b 3 ,b 4 ) which describe when the following system is consistent: 1 2 1 0 3 3 1 0 - 1 2 0 - 2 x = b (5) For which values of a and b does the vector (2 , 0 ,a,b ) lie in Span ± (1 , 0 , 1 , 2) , (2 , 3 , 0 , 0) , (1 , 3 , - 1 , - 2) ² (6) Determine if the following collections of vectors are independent or dependent: (a) (1 , 0 , 2 , 3) , (2 , 1 , 1 , 4) , (0 , 1 , 2 , 1) , (1 , 0 , - 3 , 0) (b) (2 , 1 , 2) , (1 , 1 , 1)
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This note was uploaded on 12/10/2011 for the course MATH 3000 taught by Professor Staff during the Fall '08 term at University of Georgia Athens.

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Practice_exam2 - MATH 3000 EXAM 2 PRACTICE SHEET Computation(1 Find a basis for Span(1 0 1 2(2 3 0 0(1 3 1 2(2 Find a basis for Span(1 0 1 2(2 3 0

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