homework_1 - THE CHINESE UNIVERSITY OF HONG KONG Department...

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Unformatted text preview: THE CHINESE UNIVERSITY OF HONG KONG Department of Mathematics MAT2310 Linear Algebra and Applications (Fall 2007) Homework 1 Answer all the questions. 1. Find all the solutions of the linear systems using the method of elimination. (a) x + 2 y + 3 z = 8 x + 3 y + 3 z = 10 x + 2 y + 4 z = 9 (b) x + 2 y + 3 z = 0 4 x + 5 y + 6 z = 0 7 x + 8 y + 10 z = 0 2. Let A = • 1 2 3 4 ‚ and B = •- 1 5- 2 ‚ . Compute (2 A + B )( A- 3 B ) and 2 A 2- 5 AB- 3 B 2 . Are these equal? What is the correct expansion of (2 A + B )( A- 3 B )? 3. Find an equation involving a , b , and c that makes the augmented matrix correspond to a consistent system: 2 5- 3 a 4 7- 4 b- 6- 3 1 c 4. Use elementary row operations to find the inverses of the given matrices A , if possible (a) A = 3 4 1- 1 4- 1 3 5 1 5- 4- 6 4- 3 2- 2 (b) A = 2 1 3 3 3 5 4 6 5- 5 4 2- 4 9- 3 1 5. Find an LU-factorization of the coefficient matrix of the given coefficient matrix of...
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homework_1 - THE CHINESE UNIVERSITY OF HONG KONG Department...

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