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20fmid2 - Math 20F Test 2 100 points-Notation All scalars...

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Math 20F Test 2 100 points February 25, 2009 --------------------------------------------------------------------------------------------------- Notation: A ll scalars and matrix entries and polynomial coefficents are in the set R of real numbers. Points: Problems (1) , (3), (5), (6ii) 18 pts each ; (2), (4) 10 pts each ; (6i) 8 pts Directions: Show all work and justify all answers. ----------------------------------------------------------------------------------------------------- (1) Find a basis for the column space CS(A), where A denotes the 4 by 4 matrix 1 2 4 6 2 4 3 2 3 6 4 2 4 8 8 8 ------------------------------------------------------------------------------------------------------- (2) True or false: The determinant of the 4 by 4 matrix A in problem (1) equals zero. ------------------------------------------------------------------------------------------------------- (3) Let A be a particular 3 by 3 matrix whose column space CS(A), viewed geometrically, is a line through the origin. True or False: The null space NS(A) of this matrix A, viewed geometrically, must be a plane through the origin. --------------------------------------------------------------------------------------------------------
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