math 235 hw2 - Homework 2, Due February 18 Adam Gamzon...

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Unformatted text preview: Homework 2, Due February 18 Adam Gamzon Related reading: sections 1.3 - 2.3 from the text 1. Determine whether or not 3 5 6 is a linear combination of 1 3 2 , 2 6 4 and - 1- 3- 2 . Solution: We must solve the linear system 3 5 6 = a 1 3 2 + b 2 6 4 + c - 1- 3- 2 . Form the augmented matrix for the system and apply Gauss-Jordan elimination: 1 2- 1 | 3 3 6- 3 | 5 2 4- 2 | 6 1 2- 1 | 3 0 0 | - 4 0 0 | 1 2- 1 | 3 0 0 | 1 0 0 | . This shows that there are no solutions to this system. Hence 3 5 6 is not a linear combination of 1 3 2 , 2 6 4 and - 1- 3- 2 . 2. Consider the linear transformation T : R 3 R 2 where T 1 = 9 6 ,T 1 = 2 3 , and T 1 = 3- 7 ....
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This note was uploaded on 11/22/2011 for the course MATH 255 taught by Professor Staff during the Spring '10 term at UMass (Amherst).

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math 235 hw2 - Homework 2, Due February 18 Adam Gamzon...

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