11hw3 - Homework Assignment #3 11.14 Which of the following...

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Unformatted text preview: Homework Assignment #3 11.14 Which of the following are bases of R 3 ? a ) 1 1 1 , 1 2 1 ; b ) 1 1 1 , 1 2 1 , 1 1 ; c ) 6 3 9 , 5 2 8 , 4 1 7 ; d ) 1 1 1 , 1 2 1 , 1 ; e ) 1 1 1 , 1 2 1 , 1 , 1 . Answer: a ) Not a basis. Two vectors cannot span R 3 (Thm. 11.6). b ) Not a basis. Label the vectors v 1 , v 2 , and v 3 . The vectors are linearly dependent since 2 v 1- v 2- v 3 = . c ) Not a basis. Form the matrix whose columns are the three vectors. Its determinant is 0. Since the matrix is not invertible, the vectors do not form a basis (Thm. 11.8). d ) It is a basis. Form the matrix whose columns are the three vectors. Its determinant is- 1. Since the matrix is invertible, the vectors form a basis (Thm. 11.8)....
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This note was uploaded on 01/01/2012 for the course ECO 7405 taught by Professor Staff during the Fall '08 term at FIU.

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