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posted by  BARCA on 10/11/2008 3:18:21 AM  |  status: Live  

help 7c p 145

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Question Details:
show that the given vectors are linearly independent in C [0,1]


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posted by problem solver on 10/11/2008 3:46:15 AM  |  status: Live
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Response Details:
Three vectors are linearly independent if the wronskian in non-zero

Here the wronskian is 
   |  1    ex + e-x  ex - e-x |
   |  0    ex  - e-x  ex+ e-x |  
   |  0    ex + e-x  ex - e-x | 
     from Principles of determinant calculation 
    Expanding along First column 
     1 * |   ex  - e-x  ex+ e-x |
=         |   ex+ e-x   ex - e-x | 

=  -4 
Which is not equal to zero 

Hence the vectors are linearly independent 

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