# Lecture 15 slides Linear Algebra.pdf - LINEAR ALGEBRA...

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LINEAR ALGEBRASLIDESLecture 15Spring 2021Harry W. McLaughlini
IntroductionThis is a brief lecture; it is devoted to “How to preparefor Exam #2”1
Exam ReferenceRoughly speaking the reference for Exam #2 includesall of lectures following those referenced for Exam #1.However the reference for Exam #2 does include Lec-ture #4 (Inner Products). A list of for Exam #2 isLectures9101112131444.14.24.34.42
Prominent TakeawaysWhat are they?Sample calculations?eigenvalues/vectorsprincipal componentsinner productsRiesz Representation TheoremadjointsQR-factorizations3
Exam FormatProblem #1 (35 pts.) partial credit awardedProblem #2 (35 pts.) partial credit awardedProblem #3 (30 pts)(a) 5 pts. no partial credit(b) 5 pts. no partial credit(c) 5 pts. no partial credit(d) 5 pts. no partial credit(e) 5 pts. no partial credit(f) 5 pts. no partial credit(g) 5 pts. no partial credit(h) 5 pts. no partial credit4
Advanced PreparationOne of the first two problems on Exam #2 will read:ProblemLetP2denote the three dimensional vector space con-sisting of all quadratic polynomials overRendowedwith the inner product,·idefined byhp, qi=Z10p(x)q(x)dx,p, q∈ P2.Using the Gram-Schmidt process on the basis, 1, x, x2
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