HW1-1 - ECE 493 Univ of Illinois HW#1 – Version 1.00 Due...

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Unformatted text preview: ECE 493 Univ. of Illinois HW #1 – Version 1.00 February 24, 2011 Due Thur, Mar 3 Spring 2011 Prof. Allen Topic of this homework: LinearAlgebra(Inverse of matrix, Cramer’s law, Gauss elimination, computing determinant) Deliverables: You best attempt at the questions. It is not in your best interest to answer questions you don’t understand (e.g., don’t copy stuﬀ from Wikipedia). 1. P407 1-(h) Derive the solution set for each of the following systems using Gauss elimination and augmented matrix format. Document each step(e.g. 1nd row → 2nd row → + 5 times 1st row), and classify the result(e.g. unique solution, the system is inconsistent, 3 parameter family of solutions, etc.) x1 + x2 − 2x3 = 3 x1 − x2 − 3x3 = 1 x1 − 3x2 − 4x3 = −1 2. P493 2-(e) Evaluate the determinant of given matrix using a cofactor expansion about the ﬁrst and last rows, and also about the last column. 123 234 345 3. Vandermonde determinant Show that for the real numbers x1 ,x2 , · · · xn , 1 x1 · · · 1 x2 · · · ··· 1 xn · · · = i<j n x1 −1 n x2 −1 n xn−1 (xj − xi ). 4. P522 1-(f )Compute the inverse of the given matrix. If it doesn’t exist, explain why. 12 1 2 1 3 0 3 −1 5. P523 5.(a),(d) Solve for x1 , x2 by Cramer’s rule. (a) x1 + 4x2 = 0, 3x1 − x2 = 6 (d) x1 + 2x2 + 3x3 = 9, x1 + 4x2 = 6, x1 − 5x3 = 2 Version 1.00 February 24, 2011 ˜ /493/Assignments/HW #1 – Version 1.00 February 24, 2011 ...
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This note was uploaded on 03/28/2011 for the course ECE ECE 493 taught by Professor Jontb.allen during the Spring '11 term at University of Illinois at Urbana–Champaign.

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