### Fermat Numbers

The Fermat numbers are numbers of the form 2 ^2n + 1 = Φn . Prove that if n < m , then Φn │ϕ m - 2. The Fermat numbers are numbers of the form 2 ^2n + 1 = (Phi)n . Prove that if n < m , then (Phi)n │(Phi)m - 2.

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The Fermat numbers are numbers of the form 2 ^2n + 1 = Φn . Prove that if n < m , then Φn │ϕ m - 2. The Fermat numbers are numbers of the form 2 ^2n + 1 = (Phi)n . Prove that if n < m , then (Phi)n │(Phi)m - 2.

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Compute the Wronskian of the given set of functions, then determine whether the function is linearly dependent or linearly independent: x^2 - x, x^2 + x, x^2, all x

Problem attached. (a) Find the shortest and the largest distance from the origin to the surface of the ellipsoid. (b) Find the principal axes of the ellipsoid.

Please see the attached file for the fully formatted problems. Use the inverse power method to estimate the eigenvector corresponding to the eigenvalue with smallest absolute value for the matrix -1 -2 -1 A= -2 -4 -3 2 2 1 where X0= [1,1,-1]. In finding A-1 use exact arithmetic with fractions. ln applyi

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I have difficulty in determining whether the signals are memoryless or causal. Please see the attached file for full problem description.

Find the linear velocity of a point on the edge of a drum rotating 52 times per minute. The diameter of the wheel is 16.0in. Please show me all the steps thank you

I have two questions that I need help with. 1) How would you find a basis of the kernel, a basis of the image and determine the dimension of each for this matrix? The matrix is in the attachment. 2) Are the following 3 vectors linearly dependent? (see attachment for the three vectors) How can you decide? I hope y

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Vector Space and Subspaces Euclidian 3-space Problem:- Show that the vectors u1 = (1,2,3), u2 = (0,1,2), u3 = (2,0,1) generate R3(R).

Find the eigenvalues of the following matrix Q = Mat[0 0 -2; 1 2 1; 1 0 1]. (See attached file for clearer version.)

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I would like a short explanation of Gaussian Elimination with partial pivoting and Gauss-Seidel. Also, explain when each applies or when one is better than the other. Please include some examples.

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Show that the functions x and x^2 are orthogonal in P5 with inner product defined by ( <p,q>=sum from i=1 to n of p(xi)*q*(xi) ) where xi=(i-3)/2 for i=1,...,5. Show that ||X||1=sum i=1 to n of the absolute value of Xi. Show that ||x||infinity= max (1<=i<=n) of the absolute value of Xi. Thank you for your explanation.

Given a vector w, the inner product of R^n is defined by: <x,y>=Summation from i=1 to n (xi,yi,wi) [a] Using this equation with weight vector w=(1/4,1/2,1/4)^t to define an inner product for R^3 and let x=(1,1,1)^T and y=(-5,1,3)^T Show that x and y are orthogonal with respect to this inner product. Compute the values of

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S_5 = Aut(A_5)

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