Flashcards in UNIT 3 Deck (32)

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1

## If a matrix is order 2x3 how many rows and colums does it have?

### 2 rows and 3 columns

2

## What element does A12 refer to?

### 1st row second column

3

## What is a square matrix?

### Has the same number of rows as columns

4

## Where does the main diagonal run?

### Top left to bottom right

5

## What is a zero matrix?

### Each element is Zero

6

## What is an equal matrix?

### When the order and each element is equal

7

## What is the transpose of a matrix?

### When the rows become columns.

8

## When is a matrix symmetric?

### When matrix 'A' = The transpose of matrix 'A'

9

## When is a matrix skew-symmetric?

### When the transpose of matrix 'A' = -A and the main diagonal consists of zeros.

10

## What is the condition for adding matrices together?

### They must be in the same order

11

## How do you subtract matrices?

### Use addition but add the negative of the matrix you are taking away. e.g A-B= A+ (-B)

12

## How do you multiply a matrix by a real number?

### Multiply each element by the number

13

## What are the transpose properties?

###
(A')'=A

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

14

## What is the condition for a product of two matrices to exist?

### The number of columns in the first matrix has to equal the number of rows in the second matrix

15

## When calculating the product of two vectors what do the outside numbers indicate? (3x2 and 2x4)

### The order of the resulting matrix (3x4)

16

## (AB)C=

### A(BC)

17

## What does A(B+C) =

### AB + AC

18

## PQ does not equal

### QP

19

## What is the identity matrix? (I)

### A square matrix where the main diagonal is 1's and the rest of the numbers are zero's

20

## If an inverse matrix exists what is AB?

### =BA=I

21

## How can you determine the inverse of a 2x2 matrix?

###
1/(ad-bc) {d-b}

{-ca}

22

## What is the determinant for a 2x2 matrix?

### ad-bc

23

## What does it mean if the determinant of a 2x2 matrix is 0?

### It is called a singular matrix because it does not have an inverse

24

## What does it mean if the determinant of a 2x2 matrix is not 0?

### It has an inverse and is called a non-singular matrix

25

## (AB)^-1=

### (B^-1)(A^-1)

26

## det (AB) =

### det A x det B

27

## What are the stages of finding the inverse to a matrix using E.R.O's?

###
Make top left entry 1 and the entries below it 0

Make the second entry in the main diagonal 1 and the entry below it 0

Make the last entry of the main diagonal 1

Make the entries above this 1 zero

Make the last number that isn't in the main diagonal a zero

28

## A(A)-1 =

### I

29

## What is AX=B rearranged to? (when finding an inverse matrix)

### X=A^-1 B

30