solutions10_2011 - Math 152, Spring 2011 Solutions...

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Unformatted text preview: Math 152, Spring 2011 Solutions Assignment #10 1. Consider the complex linear system: x 1- 2 ix 2 = 3 i- x 1 + 3 x 2 =- 2 All complex numbers appearing in your final answers of the following questions must be in the form a + bi with a,b real numbers. (a) Write the system in the form A x = b where A is a matrix with complex entries and b is a vector with complex coordinates. (b) Compute det A . (c) Compute A- 1 . (d) Use the previous question to solve the original system. (e) What MATLAB commands would enter the matrix A and compute its inverse? Solution: (a) A = C 1- 2 i- 1 3 D and b = C 3 i- 2 D . (b) det A = 1 3- (- 1) (- 2 i ) = 3- 2 i . (c) Since det A = 3- 2 i = 0, A is invertible and the formula for inverse of 2 2 matrices gives A- 1 = 1 3- 2 i C 3 2 i 1 1 D = 3 + 2 i | 3- 2 i | 2 C 3 2 i 1 1 D = 3 + 2 i 13 C 3 2 i 1 1 D and so A- 1 = 1 13 C 9 + 6 i- 4 + 6 i 3 + 2 i 3 + 2 i D . 1 (d) Since A x = b and A is invertible, we have a unique solution to the system: x = A- 1 b = 1 13 C 9 + 6 i- 4 + 6 i 3 + 2 i 3 + 2 i DC 3 i- 2 D = 1 13 C 27 i- 18 + 8- 12 i 9 i- 6- 6- 4 i D = 1 13 C- 10 + 15 i- 12 + 5 i D , that is x 1 =- 10 13 + 15 13 i and x 2 =- 12 13 + 5 13 i...
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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 The University of British Columbia.

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solutions10_2011 - Math 152, Spring 2011 Solutions...

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