Math 218 Final Exam with Questions and Answers
Eigenvectors can only occur if matrix is ANSWER square
Eigenvector formula ANSWER Av=λv
Euler characteristic ANSWER x(g) = nodes - arrows
x(g) = connected components - circuit rank
Net Flow ANSWER weights IN - weights OUT
Incidence Mat...
Math 218 Final Exam with Questions and
Answers
Eigenvectors can only occur if matrix is ANSWER square
Eigenvector formula ANSWER Av=λv
Euler characteristic ANSWER x(g) = nodes - arrows
x(g) = connected components - circuit rank
Net Flow ANSWER weights IN - weights OUT
Incidence Matrix ANSWER Nodes x Arrows
Coordinates of Arrow ANSWER [x2 - x1] = v1
[y2 - y1]= v2
Length of a vector ANSWER sqrt(x^2+y^2+z^2)
||c * v|| ANSWER |c| * ||v||
Unit vector ANSWER Vector with length 1
Normalization formula ANSWER 1/||v||
Law of Cosines ANSWER <v,w> = ||v|| * ||w|| * cos(θ)
, Acute conditions ANSWER <v,w> greater than 0
Obtuse ANSWER <v,w> less than 0
Column Perspective ANSWER AB = [Ab1 Ab2 Ab3]
Row perspective ANSWER ( i,j ) entry of product = <ith row of A, jth column B>
(AB)ˆT ANSWER BˆT AˆT
Adjoint Property ANSWER <Av,w> = <v,AˆTw>
Gramian ANSWER AˆTA
Row Echelon Form ANSWER Like RREF, but pivots DON'T have to equal 1 & only entries
BELOW pivot must equal 0
Consistent System ANSWER No pivot in augmented column,
1 solution (nullity = 0)
Infinite solutions (nullity > 0)
Inconsistent ANSWER Pivot in augmented column, NO solutions
Solving reduced systems ANSWER Ax = b
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