FINAL EXAM discrete maths

Question 1

tautology

Answer 1

always true

Question 2

contradiction

Answer 2

always false

Question 3

contingency

Answer 3

True or False

Question 4

nCr used when?

Answer 4

choosing r number of items from a total set of n

Question 5

repetition

Answer 5

n!/(r!*r2!)

Question 6

determinant

Answer 6

ad-bc

Question 7

A^-1=

Answer 7

1/D(d,-b,-c,a]

Question 8

To find matrix solution

Answer 8

x=Inverse of A * b (use dot product rule)

Question 9

if D!=0

Answer 9

, non singular, has an inverse

Question 10

magnitude of vector v=<a,b>

Answer 10

square root of a^2+b^2

Question 11

dot product

Answer 11

v.w=(ac)+(bd)

Question 12

dot product (with cos)

Answer 12

magnitude of v * magnitude of w* cos(theta)

Question 13

if 2 vectors are orthogonal

Answer 13

dot product =0, cos 90 =0 (perpendicular)

Question 14

first order linear difference equation (inhomogoneous)

Answer 14

y(n)=a*y(n-1)+b(n)

Question 15

general solution for linear difference

Answer 15

a^n * y(0)

Question 16

general solution for b(n)

Answer 16

replacement of equation (NOT general solution), solve for D

Question 17

when finding overall general solution:

Answer 17

a^n*k-D (substitute y(0), solve for k)

Question 18

shortest path

Answer 18

bellman algorithm