Re: Linear Dependence problem

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Posted by Brad Paul on October 10, 2002 at 20:13:10:

In Reply to: Re: Linear Dependence problem posted by Brad Paul on October 10, 2002 at 20:09:33:

: : I need to determine whether the given pair of functions is linearly indep or dependent. How do I do it here.. use the wronskian?

: : f(t) = e^(At)cos(Bt)
: : g(t) = e^(At)sin(Bt)

: : A & B are constants, and B != 0

: Yes use the Wronskian.

: | f(t) g(t) |
: | | =W
: | f'(t) g'(t) |

:
: If W!=0 then f(t) and g(t) are independent.

: if W=0 over a range of t then f and g are dependent over this range.

The formating is lost in the previous reply.

The odd thing of f's and g's was meant to be a determinant with f and g
in the top row and f' and g' in the bottom row. But I'm sure you know that.

Follow Ups:

Re: Linear Dependence problem Colin 22:09:43 10/10/02 (4)
- Re: Linear Dependence problem Brad Paul 08:19:22 10/11/02 (0)
- Re: Linear Dependence problem Brad Paul 07:47:41 10/11/02 (2)
  - Re: Linear Dependence problem colin 12:59:46 10/11/02 (1)
    - Re: Linear Dependence problem Brad Paul 15:48:08 10/11/02 (0)

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Comments:
: : : I need to determine whether the given pair of functions is linearly indep or dependent. How do I do it here.. use the wronskian? : : : f(t) = e^(At)cos(Bt) : : : g(t) = e^(At)sin(Bt) : : : A & B are constants, and B != 0 : : Yes use the Wronskian. : : | f(t) g(t) | : : | | =W : : | f'(t) g'(t) | : : : : If W!=0 then f(t) and g(t) are independent. : : if W=0 over a range of t then f and g are dependent over this range. : The formating is lost in the previous reply. : The odd thing of f's and g's was meant to be a determinant with f and g : in the top row and f' and g' in the bottom row. But I'm sure you know that.

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