hw6_revised2011

hw6_revised2011 - HOMEWORK 6 MATRIX OPERATIONS 1 Construct...

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1 HOMEWORK – 6 MATRIX OPERATIONS 1. Construct a 3 x 3 matrix whose elements are: a. a ij = i + j b. a ij = i * j 2. Find the values of x, y and z if: 2 ° 3 ° − ± 2 ² + ± 3 ² − ° ³ = ´ 12 6 34 9 µ 3. If A = ´ 3 7 5 9 µ , B = ´ 12 4 3 4 µ , C = ´ 3 2 4 0 µ , find each of the following: a. -2A – (B + C) b. A – (4B + C) c. A + (B + C) d. (A + B) + C e. BC f. CB 4. Find the matrix C if A = ´ 3 7 2 5 µ , B = ´ 3 2 4 1 µ , and 5C + 2B = A. 5. If A = ´ 3 5 4 2 µ , show that A 2 – 5A – 14I = 0 where I = ´ 1 0 0 1 µ . 6. Given A = · 0 ¸ 0 ¹ 2 ¸ · ¹ ¸ º and X = · ¹ 0 ¸ 2 ¹ 0 º where a, b, and c are non-zero constants: a. Find [A] * [X]. b. Find the determinant of the matrix A. c. Find the determinant of the matrix X. d. Find [A] + [X] 7. Given A = 3 2 0 4 5 7 2 6 9 º , B = 1 12 6 3 5 2 1 6 8 º , and C = 1 1 3 2 1 2 1 1 1 º , verify the following using an Excel spreadsheet: a. A * B B * A b. (A * B ) * C = A * (B * C) c. A * (B + C) = A * B + A * C 8. Hand calculate the determinant of the following matrix: » 2 3 3 1 1 1 1 5 1 2 2
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This note was uploaded on 11/14/2011 for the course CE 3010 taught by Professor Clement during the Fall '09 term at Auburn University.

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hw6_revised2011 - HOMEWORK 6 MATRIX OPERATIONS 1 Construct...

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