Recent content by sylar

Today in the lecture we have learned the Putzer Algorithm, which enables us to calculate the higher powers(A^n, n>1 an integer) of a square matrix A. The other well-known methods use the Cayley-Hamilton Theorem, and the Jordan form of a matrix. I wonder whether there are other efficient ways to...

The results of this problem are quite interesting to me. When k is an even integer, say 2n, then the number of such ways is C(2n n); and when k is an odd integer, say 2n+1, the number of such ways is C(2n+1 n). Also i found that for k odd, say 2n+1, the number of ways to realize our aim is...

Sorry for the delayed response. First, i want to thank all the posters who commented on these problem. Second, i admit that i misunderstood the problem and what i wrote here was not true. (Though still I'm right with the definition of an increasing sequence:smile:) The statement to prove is: In...

Hey guys, i think you are missing one point. The question doesn't ask us to prove that there exists a strictly increasing sequence; it asks us to show that there exists an increasing sequence. That is, if all terms are equal to each other, then we have an increasing sequence. Here is the...

In a sequence with 101 elements show that one can find an increasing sequence of 11 terms. Here is my approach: Pick the greatest element of the sequence (or one of the largest elements if there is more than one large element) and put it onto the end of the sequence we are forming. Then make...

Since x(t)=k doesn't have a term including t, we have dx/dt=0.The rest is just simple arithmetic!

Homework Statement In how many ways can we form a sequence of non-negative integers a_1,a_2,...,a_(k+1) such that the difference between the successive terms is 1 (any of them can be bigger) and a_1 =0. Homework Equations The Attempt at a Solution For k=1, there is only one...

The answer of the first question is x*((ln x)^2) - 2x*(ln x) + 2x , you can check your answer. As for the second one, my approach would be to write the integrand as ((cos x)^2)*(1 - ((sin x)^2)) , and then finish this off by using the trigonometric identities for (cos x)^2 and sin 2x ...

Here since this is continuous random variable, we can define f(9)=1. Then looking at the graph of x-f(x), we see that the expected value is the sum of the areas under the curve. Hence, for this question the expected value is ((10-8)*1)/2=1, which proves that f is a probability function.

Let X be a set with n elements, and let A,B be subsets of X. What is the general expected value for the intersection of these two sets? Here for each n, we must find the possibility of having an intersection set of elements, multiply this probability by n, and then sum up the products we...