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#1 Help Me ! » Calculus Question » 2007-05-10 00:50:11

corvax235
Replies: 1

The functions A(t) and B(t) are solutions to this system of differential equations:

x' = y
y' = x
x(0) = 1
y(0) = 0

Find and classify all equilibrium points of this system.

#2 Re: Help Me ! » Linear transformation problem » 2007-05-09 18:01:17

Is there a way I can just use Mathematica to figure out the matrix?

#3 Re: Help Me ! » Linear transformation problem » 2007-05-07 14:44:15

You know where I have all the x's filled in?  How do I know what numbers to put in place of those?

#4 Re: Help Me ! » Linear transformation problem » 2007-05-07 14:29:16

L is:

L(

) = (-10, 5, 0, 9)
L(
) = (0, 1, 0, 17)
L(
) = (-1, 0, 2, 0)
L(
) = (2, -1, 1, 2)

L(

) = (-10, 5, 0, 9)  = x*(7, 0, -3, 1) + x * (2, -1, -2, 2) + x * (-2, 0, 1, 0) + x * (5, 17, 0, 0)
L(
) = (0, 1, 0, 17) = x*(7, 0, -3, 1) + x * (2, -1, -2, 2) + x * (-2, 0, 1, 0) + x * (5, 17, 0, 0)
L(
) = (-1, 0, 2, 0) = x*(7, 0, -3, 1) + x * (2, -1, -2, 2) + x * (-2, 0, 1, 0) + x * (5, 17, 0, 0)
L(
) = (2, -1, 1, 2) = x*(7, 0, -3, 1) + x * (2, -1, -2, 2) + x * (-2, 0, 1, 0) + x * (5, 17, 0, 0)

#5 Re: Help Me ! » Linear transformation problem » 2007-05-07 13:55:59

Sorry I'm confused - how does
{

,
,
,
} fit into this?

#6 Re: Help Me ! » Linear transformation problem » 2007-05-07 13:42:43

Ah sorry, I forgot to include the linear transformation L

L of
(a  b
c  d)
=

(-10a - c + 2d, 5a + b - d, 2c + d, 9a + 17b + 2d)

#7 Re: Help Me ! » Linear transformation problem » 2007-05-07 12:08:19

I'm having trouble getting started.

#8 Help Me ! » Linear transformation problem » 2007-05-06 16:40:27

corvax235
Replies: 12

Consider M_22 with the basis

{

,
,
,
}

and consider R^4 with the basis

.  Find the matrix which corresponds to the linear transformation L with respect to these two bases.

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