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It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system,
x?' = A x?
Here the eigenvalues of the matrix A are complex. By using complex eigenvalues we are going to have similar problem that we had back while we were looking at second order differential equations. We need our solutions to only have real numbers in them, though as our solutions to systems are of the form,
x?1 = ?h elt
We are going to contain complex numbers come in our solution from both the eigenvector and the eigenvalue. Getting rid of the complex numbers now will be same to how we did this back in the second order differential equation case, although will include a little more work this time around. It's simple to see how to do it in an example.
Laura paid $17 for a pair of jeans. The ticketed price was 20% off the original price plus the sign on the rack said, "Take an additional 15% off the ticketed price." What was the
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Chain Rule : If f(x) and g(x) are both differentiable functions and we describe F(x) = (f. g)(x) so the derivative of F(x) is F′(x) = f ′(g(x)) g′(x). Proof We will s
S-aSa;S-bSb;S-c construct an CFG
Brent covered 3 1/5 by a number and got 4 1/2 what number dis he divide by? The answer is either 1 9/16, or 32/45. Which one is the answer, and how did you get it?
Determine y′ for xy = 1 . Solution : There are in fact two solution methods for this problem. Solution 1: It is the simple way of doing the problem. Just solve for y to
265 divided by 7
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find the series of the first twenty terms
2sqrt73x
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