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Mathematik-Online problems:

Problem 150: Linearly Independent Functions

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Test, whether the following functions are linearly independent, or not:
a)
$ f_1(x)=3x^2+x+3$, $ f_2(x)=x^2-5x+5$, $ f_3(x)=2x^2+2x+1$
b)
$ f_1(x)=x$, $ f_2(x)=x^2 2^x$, $ f_3(x)=x^3 3^x$, $ f_4(x)=x^4 4^x$
c)
$ f_1(x)=1$, $ f_2(x)=\sin x$, $ f_3(x)=\cos 2x$, $ f_4(x)=\sin^2 x$
d)
$ f_1(x)={\rm {e}}^x\sinh x$, $ f_2(x)={\rm {e}}^x\cosh x$, $ f_3(x)={\rm {e}}^{-x}\sinh x$, $ f_4(x)={\rm {e}}^{-x}\cosh x$

(Authors: Apprich/Höfert)

see also:

[Solutions]
  automatisch erstellt am 14. 10. 2004