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