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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.
Given that f(x,y) = 3xy - x 2 y - xy 2 . Fi nd all the points on the surface z = f(x, y)where local maxima, local minima, or saddles occur
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find the newton raphson iterative formula for a reciprocal of a number N and hence find the value of 1/23
A standard deck of cards contains 52 cards. One card is selected at random. Determine a) The probability that the card is a 8 or an Ace? b) The probability that the card is
Rajun uses 2/3 of a carton of milk to make a pancake. The volume of milk he uses is 800ml. calculate the volume, in l, of a milk in carton?
It is totally possible that a or b could be zero and thus in 16 i the real part is zero. While the real part is zero we frequently will call the complex numbers a purely imaginar
Show that A-B ? C ? A?B ? B?C?
prove that sin A /cot A + cosec A = 2 + sinA / cot A - cosec A
Find out the roots of the following quadratic equation. 3x 2 + 7x = 0 Solution: Using Equation 6, one root is determined. x = 0 Using Equation 7, substitute the
Interpretation A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that there is a causal relationship that is
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