assig10 - system. (b) Write the MATLAB commands that would...

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Math 152, Spring 2010 Assignment #10 Notes: Each question is worth 5 marks. Due in class: Monday, March 29 for MWF sections; Tuesday, March 30 for TTh sections. Solutions will be posted Tuesday, March 30 in the afternoon. No late assignments will be accepted. 1. Simplify the following expressions so that your answers are in the form a + ib . (a) 2 1 - 3 i . (b) 2+ i 1 - i . (c) 3 - - 54 3 . (d) 3 e 2 i 2. Find the eigenvalues and the corresponding eigenvectors of the follow- ing matrix. A = ± 1 2 - 3 1 ² Please write your answers for the eigenvalues in the form λ = a + ib . 3. Consider the following system of linear equations with complex coeffi- cients and right hand sides. Note that each component of the solution vector ( x,y,z ) will be a complex number. ix + 2 y + (1 + i ) z = 1 x + (2 - i ) y + 2 z = i (1 + i ) x + 2 y + 3 iz = - 1 (a) Use Gaussian elimination with complex arithmetic to solve the
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Unformatted text preview: system. (b) Write the MATLAB commands that would solve the system, with the solution in column vector x . 4. Find all the values of a such that the matrix C = ± 2 a 1 1 ² has the value 1 as one of it’s eigenvalues. 5. Suppose that R : R 2 → R 2 is the linear transformation that corresponds to reflection with respect to the line y = x and that P : R 2 → R 2 is the linear transformation that corresponds to orthogonal projection with respect to a unit vector that makes an angle of 45 degrees with respect to the x-axis. (a) Find the eigenvalues of the matrix representing R . What is the geometric meaning of your results? (b) Find the eigenvalues of the matrix representing P . What is the geometric meaning of your results?...
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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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assig10 - system. (b) Write the MATLAB commands that would...

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