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 ...
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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