assig6_2011

# assig6_2011 - brieﬂy(a(1 mark f x,y,z = 2 x y-z 1 2(b(2...

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Math 152, Spring 2011 Assignment #6 Notes: Each question is worth 5 marks. Due in class: Monday, February 14 for MWF sections; Tuesday, Feb- ruary 15 for TTh sections. Solutions will be posted Tuesday, February 15 in the afternoon. No late assignments will be accepted. (1) Consider the resistor network given in the following picture: Use the method of loop currents to ﬁnd the current though each of the resistors and the change in voltage E across the current source (2) Consider the following matrix A = ± 1 2 1 3 ² . Find all matrices of the form B = ± a b c d ² such that AB = BA . (3) Let C = ± 2 - 1 1 1 ² and D = 2 1 0 2 - 1 3 . (a) (1 mark) Explain why the product CD is not deﬁned. (b) (2 marks) The product DC is deﬁned. Compute this product. (c) (2 marks) Solve the system of equations DC x = 0. (4) Determine if the following functions are linear transformations. Justify

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Unformatted text preview: brieﬂy. (a) (1 mark) f ( x,y,z ) = 2 x + y-z . 1 2 (b) (2 marks) g ( x ) = ( x, cos( x )). (c) (2 marks) h ( x,y ) = (2 x + 3 y,x-y ). (5) Consider the matrix E = ± 0 1 0 0 ² . (a) (1 mark) Show that E 2 = 0. (b) (3 marks) Compute ( E + I ) 4 , where I is the 2 × 2 identity matrix. ( Hint . You can compute this directly or use the following: If A and B are two square matrices of the same size such that AB = BA then one can use the binomial formula to compute ( A + B ) n for any n ≥ 0.) (c) (1 mark) What MATLAB commands would you enter to compute ( E + I ) 4 for the question above? You may assume that E has been entered already....
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assig6_2011 - brieﬂy(a(1 mark f x,y,z = 2 x y-z 1 2(b(2...

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