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Math 218 Final Questions And Answers Latest Update
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Math 218 Final Questions And Answers Latest Update
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Solution 2024/2025Pepper
Math 218 Final Questions And Answers Latest
Update
Eigenvectors can only occur if matrix is ANS✔✔ square
Eigenvector formula ANS✔✔ Av=λv
Euler characteristic ANS✔✔ x(g) = nodes - arrows
x(g) = connected components - circuit rank
Net Flow ANS✔✔ weights IN - weights OUT
Incidence Matrix ANS✔✔ Nodes x Arrows
Coordinates of Arrow ANS✔✔ [x2 - x1] = v1
[y2 - y1]= v2
Length of a vector ANS✔✔ sqrt(x^2+y^2+z^2)
||c * v|| ANS✔✔ |c| * ||v||
Unit vector ANS✔✔ Vector with length 1
, Solution 2024/2025
Pepper
Normalization formula ANS✔✔ 1/||v||
Law of Cosines ANS✔✔ <v,w> = ||v|| * ||w|| * cos(θ)
Acute conditions ANS✔✔ <v,w> greater than 0
Obtuse ANS✔✔ <v,w> less than 0
Column Perspective ANS✔✔ AB = [Ab1 Ab2 Ab3]
Row perspective ANS✔✔ ( i,j ) entry of product = <ith row of A, jth column
B>
(AB)ˆT ANS✔✔ BˆT AˆT
Adjoint Property ANS✔✔ <Av,w> = <v,AˆTw>
Gramian ANS✔✔ AˆTA
Row Echelon Form ANS✔✔ Like RREF, but pivots DON'T have to equal 1 &
only entries BELOW pivot must equal 0
Consistent System ANS✔✔ No pivot in augmented column,
1 solution (nullity = 0)
Infinite solutions (nullity > 0)
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