The Eigenvalues and Eigenvectors of are
1.
2.
3.
Therefore we can write
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The Eigenvalues and Eigenvectors of are
1.
2.
3.
Therefore we can write
----
Thus we have
Therefore,
Similarly,
Therefore,
Therefore,
Let
Then
Since we require that
This requires that
Then we have
Now,
Thus we have
2. (14pts) Diagonalize the following matrices, B = [ 4 1 1 1] 1 4 1 1 A= 1 1 4 1 1 1 1 4 Find formulas for Ak, Bk, k > 1. [ 4 0 | 0 4 0 0 | 1 0 0 0 1 0 0 2 0 0 2
A cylindrical conductor of a circular cross section (radius = a) carries a time-invariant current I(>0) directed out of the page. The line integral of the magnetic flux density vector B, along a closed circular contour C positioned inside the conductor (the contour radius r is smaller than the conductor radius a) is conductor
Consider that V = R3 and W = {(a,b,c): a > 0} List 5 elements of W Is W a vector subspace? Justify
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
Proposition 7.27. Suppose fn: G + C is continuous, for n > 1, (fn) converges uniformly to f :G+C, and y C G is a piecewise smooth path. Then lim n-00 $. fn = $. . 7.23. Let fn(x) = n2x e-nx. (a) Show that limn400 fn(x) = 0 for all x > 0. (Hint: Treat x = O as a special case; for x > 0 you can use L'Hôspital's rule (Theorem A.11) — but remember that n is...
{x_n} and {y_n} are sequences of positive real numbers AC fn→oo > O, prove tha m in yn lim xn 0 implies lim yn_0
What can you summarize from the given information. the convergence of an (an > 0 for all n.) n= 1 n lim no = 0.95 an
Help please! Let Be be Brownian motion and fix to > 0. Prove that By: = Bto+t - Blo; t o is a Brownian motion.
Vx+1-1 Evaluate: lim x>0 х Please solve it in detail and show all your steps./
Please prove this, thanks! 2. Let {xn n21 be a sequence in R such that all n > 0. If ( lim supra) . (lim supー) = 1 Tn (here we already assume both factors are finite), prove that converges.