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Flashcards in Term 1 Deck (25):
1

What is the check for Linear Dependence?

Can be wrote as a linear combination of the others, using scalars

2

What are the properties of transposes?

(A')' = A
(A + B)' = A' + B'
(AB)' = B' A'

3

What are the key properties of multiplication and addition?

Adding:
Commuttative: A+B=B+A
Both:
Associative: (A+B)+C=A+(B+C)
Multiplication
Distributive:(A+B)C=AC+BC

4

What is an identitiy matrix?

Diagonal ones, rest zero

5

What is a null matrix?

All zero

6

What is an indepotent matrix?

A*A=A

7

What is a diagonal Matrix?

Identity but with numbers other than 1

8

What is a triangular matrix?

All numbers one side of diagonal are not zero, rest are zero

9

What is Row Echelon Form?

All non zero rows are above all zero rows
Each leading entry is to the right of the entry above
All other entrys below are zero

10

What are the three ERO?

Interchanging two rows
Multiplying a row by a nonzero constant
Adding a multiple of a row to another row

11

How do you calculate the inverse of a 2x2?

Switch principal diagonals, negate others, divide by determinant

12

What are the properties of inverses?

(A^-1)^-1=A
(AB)^-1=A^-1*B^-1
(A')^-1=(A^-1)'

13

How do you find the determinant of a square matrix?

Multiply the Diagonal

14

How can you find the determinant of a 3x3 or greater?

Use ERO to transform A to an identity matrix with a copy
Use cofactor method

15

How do you find a rank?

Largest nonzero determinant square matrix
Use ERO to move to row echelon, rank is number of non-zero rows

16

What does a rank determine in a homogeneous system

If r(A) < Number of unkowns : Infinite sollutions
If r(A) =n : Only trivial sollution

17

What is the test for consistency

If R(A|B)=R(A) system is consistent and has solutions

18

How do you find an eigine value?

A-LamdaI = 0 and solve

19

How do you find an eigine vector

Put eigine value back into original and solve

20

How do you create an input output model?

Collums are output
Rows are the same commodity

21

In unconstrained optimisation, what is the SOC?

Max: Fxx<0, Fyy<0, FxxFyy-(Fxy)^2>0

Min: Fxx>0, Fyy>0, FxxFyy-(Fxy)^2>0

22

When using the Hessian, what is the SOC?

Negative Def: Fxx<0, H2x2>0 H3x3>0...

Positive Def: All > 0

23

When using the Bordered Hessian, what is the SOC?

If H>0, negative def
If H<0 Positive Def

24

What form must the constraint be wrote in?

X<=Y

25

What is the SOC for constricted inequality optimisation?

IF Lamda>0:
C-g(X,y) = 0 with Li=Fi-LamdaGi

IF Lamda=0 Li=Fi=0