Eng Math Exam: Algebra - Analysis - K-Filters

EGR 1010 Engineering Mathematics

Question:

The topic will be abstract linear algebra, real analysis, Kalman filter\'s and numerical analysis. I will send pdf on the exam date. Exam Date : 16 December 2021 12:00 PM Subject : Engineering Mathematics Exam Duration : 3 hour No Of Question : 10 Type Of Question : analysis No of Attempts : 1 University Url : www.google.com University Username : as University Password : as

X = P(t) = {set of polynomials with real coecients}. F = R. Claim: The monomials are linearly independent. In particular, for each n ? 0, the set {1, t, . . . , tn} is linearly independent.

1. (X , F), F = R, X = {f : (??,?) ? R}, Y = {polynomials with real coecients} Is Y a subspace? Yes, by part 2 of the proposition.

2. Let X = {f : R ? R} and F = R. S = {1, t, t2 , . . . } = {t k |k ? 0}. span{S} = P(t) = {polynomials with real coecients}.

3. The infinite set {1, t, . . . , tn , . . . } is a basis for (P(t), R).

4. Let (X , F) be an n-dimensional vector space (n is nite). Then any set of n linearly independent vectors is a basis.

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