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Math 218 Unit 1 Exam with Questions and Answers
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Math 218 Unit 1 Exam with Questions and Answers how to separate <v -w, v-w> ANSWER foil method 1. <v, v-w> - <w, v-w> 2. <v,v> - <v, w> - <w,v> - <w,w> 3. ||v||^2 + ||w||^2 - 2<v,w> another word for transpose ANSWER involution trace of a ...

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  • November 15, 2024
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  • 2024/2025
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Math 218 Unit 1 Exam with Questions and
Answers
how to separate <v -w, v-w> ANSWER foil method

1. <v, v-w> - <w, v-w>

2. <v,v> - <v, w> - <w,v> - <w,w>

3. ||v||^2 + ||w||^2 - 2<v,w>



another word for transpose ANSWER involution



trace of a matrix ANSWER sum of diagonal entries, linear operation



diagonal matrix ANSWER a square matrix whose entries not on the main diagonal are all
zero



rank one matrix ANSWER if every column is a multiple of the first nonzero column



first pivot column ANSWER first nonzero column



linear combination ANSWER A sum of scalar multiples of vectors. The scalars are called the
weights.



matrix-vector product (between AER^mxn and vER^n) things to note ANSWER - number of
A columns = number of v coordinates



linearity, identity, zero rules ANSWER linearity = A (c1v1 + c2v2) = c1Av1 + c2Av2

zero = A0n= 0m

, identity = Inv = v



Eigenvector ANSWER A nonzero vector x such that Ax = λx for some scalar λ



Eigenvalue ANSWER A scalar lambda such that Ax = lamba x has a solution for some
nonzero vector x



input/output notation ANSWER Let Matrix A exist on R^mxn, v exists on R^n (input), b
exists on R^m (output)

A(v) = b



Arrow notation ANSWER A

R^n --> R^m



vector v in R^n ANSWER has 3 rows 1 column as a matrix



how to summarize Av = lambda(v) ANSWER v exists on (E sub A)(lambda)



Digraph ANSWER directed graph



Euler characteristic ANSWER χ(G) = (Number of nodes) - (number of arrows)



Connected Component ANSWER "islands" of a digraph



path ANSWER sequence of distinct arrows joining consecutive nodes. can travel with or
against arrows, noted by Path(a1,a2,a3) connects v1 to v6

Can't reuse arrows

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