UNIT 3

Question 1

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

Answer 1

2 rows and 3 columns

Question 2

What element does A12 refer to?

Answer 2

1st row second column

Question 3

What is a square matrix?

Answer 3

Has the same number of rows as columns

Question 4

Where does the main diagonal run?

Answer 4

Top left to bottom right

Question 5

What is a zero matrix?

Answer 5

Each element is Zero

Question 6

What is an equal matrix?

Answer 6

When the order and each element is equal

Question 7

What is the transpose of a matrix?

Answer 7

When the rows become columns.

Question 8

When is a matrix symmetric?

Answer 8

When matrix ‘A’ = The transpose of matrix ‘A’

Question 9

When is a matrix skew-symmetric?

Answer 9

When the transpose of matrix ‘A’ = -A and the main diagonal consists of zeros.

Question 10

What is the condition for adding matrices together?

Answer 10

They must be in the same order

Question 11

How do you subtract matrices?

Answer 11

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

Question 12

How do you multiply a matrix by a real number?

Answer 12

Multiply each element by the number

Question 13

What are the transpose properties?

Answer 13

(A’)’=A

(A+B)’=A’+B’

Question 14

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

Answer 14

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

Question 15

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

Answer 15

The order of the resulting matrix (3x4)

Question 16

(AB)C=

Answer 16

A(BC)

Question 17

What does A(B+C) =

Answer 17

AB + AC

Question 18

PQ does not equal

Answer 18

QP

Question 19

What is the identity matrix? (I)

Answer 19

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

Question 20

If an inverse matrix exists what is AB?

Answer 20

=BA=I

Question 21

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

Answer 21

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

{-ca}

Question 22

What is the determinant for a 2x2 matrix?

Answer 22

ad-bc

Question 23

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

Answer 23

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

Question 24

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

Answer 24

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

Question 25

(AB)^-1=

Answer 25

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

Question 26

det (AB) =

Answer 26

det A x det B

Question 27

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

Answer 27

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

Question 28

A(A)-1 =

Answer 28

I

Question 29

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

Answer 29

X=A^-1 B

Question 30

How do you find the transpose of a 3x3 matrix?

Answer 30

Do the determinant calculation thing but for all rows to form a matrix, no co efficients. Signs are alternating, starting with positive.

Question 31

How do you calculate the inverse of a 3x3 matrix using the transpose and the determinant?

Answer 31

1/det A multiplied by the transpose.

Question 32

How do you find the solution of a 3x3 matrix using the inverse?

Answer 32

X=A^-1 B Where B is the column matrix consisting of the last values in the equations (solutions)