11.11 Verify Schwarz's inequality for 1-1 n= where the constants. (t)s are orthonormal and the a,s...
Exercise 11. Given th=3(1 1 1-1)" and v2-(-1 1 3 5)T, verify that these vectors form an orthonormal set in R. Extend this set to an orthonormal basis for R4 by finding an orthonormal basis for the nullspace of 1 -1 113 5 Hint: First find a basis for the null space and then use the G-S process.
Exercise 11. Given th=3(1 1 1-1)" and v2-(-1 1 3 5)T, verify that these vectors form an orthonormal set in R. Extend...
use proof by induction
Day 1. Consider the inequality n 10000n. Assume the goal is to prove that inequality is true for all positive integers n. A common mistake is to think that checking the inequality for numerous cases is enough to prove that statement is true in every case. First, verify that the inequality holds for n-1,2,-.- ,10. Next, analyze the inequality; is there a positive integer n such that the inequality n 10000n is not true!
Day 1....
r the recurrence relation o. Consider T(n) = Vn T(Vn) + n a. Why can't you solve this with the master theorem? b. S t involves a constant C, tell me what it is in terms of T(O), T(1), or whatever your inequality by induction. Show the base case. Then show the how that T( n)= 0(n lg ig n). First, clearly indicate the inequality that you wish to hen proceed to prove the inductive hypothesis inductive case, and clearly...
verify the eigenfunctions of the problem
12. (a) Verify that the eigenfunctions of the problem n are y"(x) = cos (x + π), n=0,1,2, (b) Show that the eigenfunctions in part (a) are orthogonal on , . (Hint: Use the trigonometric identity sin A cos B =-sin (A + B) +、sin (A-B).) Obtain the orthonormal set of eigenfunctions for the problem in part (a). (e)
7. Claim: Let A be an (n × n) (square) matrix. ·Claim: If A s invertible and AT = A-1 , then the columns of A form an orthonormal basis for R . Claim: If the columns of A form an orthogonal basis for Rn, then A is invertible and A A-1 . Claim: If the columns of A form an orthonormal basis for R", then A is invertible and AT= A-1 . Claim: If the columns of A form...
Find an orthonormal basis for the given subspace. (Enter sqrt(n) for n.) S = span
help with #2
(2) Verify Stokes' theorem for where s is the portion of the surface of the cone z = VF+7 : 0 2, with normal n pointing z upward"
(2) Verify Stokes' theorem for where s is the portion of the surface of the cone z = VF+7 : 0 2, with normal n pointing z upward"
Verify that S and T are inverses. S: 91 P1 defined by S(a +bx) - (-42 + b) + 2ax and T:11 defined by T(a + bx)-b/2 (a 2b)x we must verify that S。T-, and To S-1. 91 T o S)(a bx)- Thus, (S o T)(a bx) -(To S)(a + bx) - for any a bx e P1 so both compositions are the identity and we are done. Need Help?Read It Talk to a Tutor
Consider N and the set S={x∈{0,...N-1}:gcd(x,N)=1} where k=|S| For a∈S, we define T={ax(modN):x∈S}. what is |T|? Answer may include N and k.
Question 66.4 from Fourier series and Boundary value problems
Brown and Churchill
4. (a) Use the same steps as in Example 3, Sec. 61, to verify that the set of functions is orthonormal on the interval -c