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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.
Examples of logarithms: log 2 8 = 3 since 8 = 2 3 log 10 0.01 = -2 since 0.01 = 10
Explain this statement " As we begin the 21st century, the dilemmas of America's minority groups remain perhaps the primary unresolved domestic issue facing the nation." How might
A jeweler has bars of 18-carat gold and 12-carat gold. How much of every melted together to obtain a bar of 16-carat gold, weighing 120 gm ? It is given that pure gold is 24 carat.
Properties of Logarithms 1. log a xy = log a x + log a y 2. = log a x - log a y 3. log a x n = n log
the sum of the interior angles of a convex rectilinear figure is equal to sum of the exterior angles. then the number of sides is
1+1
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Three shirts and five ties cost $23. Five shirts and one tie cost $20. What is the price of one shirt? Let x = the cost of one shirt. Let y = the cost of one tie. The ?rst part
1. In 1900, a certain country's population was 77,977,459 and it's area was 2,821,924 square miles, In 2000, the country's population was 283,575,229 and its area was 3,551,003 sq
Combined Mean And Standard Deviation Occasionally we may need to combine 2 or more samples say A and B. Therefore it is essential to identify the new mean and the new standard
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