assig6

# assig6 - deﬁned matrix C . 4. Deﬁne A = ± 1 2 3 4 ² ....

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Math 152, Spring 2010 Assignment #6 Notes: Each question is worth 5 marks. Due in class: Monday, February 29 for MWF sections; Tuesday, March 1 for TTh sections. Solutions will be posted Tuesday, March 1 in the afternoon. No late assignments will be accepted. 1. For the resistor network in the picture, use loop currents to ﬁnd the current through the 4Ω resistor and the change in voltage E across the current source. 2. Suppose that the reduced row echelon form of a matrix A is 1 2 0 0 0 0 1 0 0 0 0 1 . Were the columns of A linearly dependent or independent? (HINT: consider the solution set to A~x = ~ 0.) 3. Deﬁne A = ± 1 1 1 2 2 2 ² and B = 1 1 2 2 3 3 . (a) Find AB and BA . (b) If the matrix product ACB is deﬁned, what size must C be? (c) Write the MATLAB command to enter the matrix A above. (d) Write the MATLAB command that returns the ﬁrst row of a previously

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Unformatted text preview: deﬁned matrix C . 4. Deﬁne A = ± 1 2 3 4 ² . Find a matrix B = ± a b c d ² so that AB = I . For your answer, also ﬁnd BA . 5. Deﬁne the matrices R = ± cos(90 ◦ )-sin(90 ◦ ) sin(90 ◦ ) cos(90 ◦ ) ² = ±-1 1 ² , S = ± cos(45 ◦ )-sin(45 ◦ ) sin(45 ◦ ) cos(45 ◦ ) ² = " √ 2 2-√ 2 2 √ 2 2 √ 2 2 # , and T = ± cos(180 ◦ ) sin(180 ◦ ) sin(180 ◦ )-cos(180 ◦ ) ² = ±-1 0 1 ² . (a) For a vector ~x ∈ R 2 , describe geometrically the eﬀect of multiplying ~x on the left by the matrices R , S , or T . (b) Does RS = SR ? Does this make sense given your answer to part (a)? (c) Does RT = TR ? Does this make sense given your answer to part (a)?...
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## This note was uploaded on 03/30/2011 for the course MATH 152 taught by Professor Caddmen during the Spring '08 term at UBC.

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assig6 - deﬁned matrix C . 4. Deﬁne A = ± 1 2 3 4 ² ....

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