I'm working on the same problem, to show P(k+1) I set it up the same way
but then we can use our inductive hypothesis
(1+x)^(k+1) >= (1+kx+(1/2)*k(k-1)*x^2)(1+x)
My question is, I've wrestled with the algebra for a little while now and for some reason in my notes i had P(K) set to...
two things, how should i show a prime p, divides a ex.
(p=2^e1 *3^e2 *5^e3...) = a*q?, q is an integer
And why do i need to show that it is less than or equal to the number of times p divides b?
Let R be a commutative ring. Show that the characteristic or R[x] is the same as the characteristic of R.
I'm really not sure where to start on this at all. I'm not sure what is ment by R.
Let a, b be integers a,b>0 show that if a^3 | b^2 then a|b
(Consider the prime factorization of a and b)
I've tried setting up generic prime factorization of a and b but then don't get any where, I'm not very strong at this subject.
Any kind of hints / where to start would help a lot...
I don't remember ever learning that, sorry for being clueless, but i don't see the relation.
OH, maybe since det A is the product of eigenvalues, and because 1 or -1 is the only number ^-1 that stays the same ?
is that right?
Homework Statement
Prove all eigenvalues = 1 or -1 when A is circulant and satisfying
A=A^T=A^-1
I can think of an example, the identity matrix, but i can't think of a general case or how to set up a general case.
Homework Equations
The Attempt at a Solution
I can only show by...
Hi, i need to pass a function in MATLAB a few parameters, one of the parameters is an equation such as :
sin(x)-cos(y)
and have it make the 3d graph, i have no problem setting up the meshgrid etc and getting it to work running strait from the m-file
function graph = graph(f)
n=20;
x =...
i have this code
A = [2 -2;-2 -1];
A=orth(A);
B=inv(A);
if A==B
disp('match');
else
disp('no match');
end
they are the same, but i always get the output 'no match'
any ideas?