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.
 Spring '11
 JontB.Allen

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