Prove that (F,|.|) is Banach space where FE{C, R}
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A: I have explained everything with in the solution. Please go through that.
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A: I have explained everything with in the solution. Please go through that.
Q: QUESTION 2 At x=1, the Fourier series of f(x)=exp(x), on -1<x< 1 converges to: Note: exp(A) = eA OA.…
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Q: ) Let B be a basis. Prove that [cu] = c[u] where u is a vector and c is a scalar.
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A: Ok
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Q: I want to solve the non homogeneous equation 3y^2 + 7y + 2 = e^(2t). The way I want to solve this…
A: 3y''+7y'+2y=e2t Note: Given non homogeneous equation 3y2+7y+2=e2t. Correcting it to 3y''+7y'+2y=e2t
Q: Evaluate the integral [[F.n dA for the data F= [y³, a³, 2³], S S: x² + 4y² = 4, x ≥ 0, y ≥ 0,0 ≤ z ≤…
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- Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1) is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.[Type here] 21. Prove that ifand are integral domains, then the direct sum is not an integral domain. [Type here]Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.
- [Type here] 18. Prove that only idempotent elements in an integral domain are and . [Type here]Prove that if a subring R of an integral domain D contains the unity element of D, then R is an integral domain. [Type here][Type here]Complete the proof of Theorem 5.30 by providing the following statements, where and are arbitrary elements of and ordered integral domain. If and, then. One and only one of the following statements is true: . Theorem 5.30 Properties of Suppose that is an ordered integral domain. The relation has the following properties, whereand are arbitrary elements of. If then. If and then. If and then. One and only one of the following statements is true: .
- Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}27. Let , where and are nonempty. Prove that has the property that for every subset of if and only if is one-to-one. (Compare with Exercise 15 b.). 15. b. For the mapping , show that if , then .Let V be the set of all positive real numbers. Determine whether V is a vector space with the operations shown below. x+y=xyAddition cx=xcScalar multiplication If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.