Matrices

Question 1

You can only add matrices when

Answer 1

They have the same dimensions

Question 2

How to add, subtract and multiply matrices by a scalar

Answer 2

Just do each element separately

Question 3

How to multiply matrices

Answer 3

Row x column
(A , b , c) (1).
(D, e ,f) (2)
(3)

Question 4

What is the dimension rule for multiplying matrices

Answer 4

A(Column x row) x B(column x row)
A(row) = B(column)

Question 5

What is the identity matrix

Answer 5

1 0
0 1

Question 6

What is an identity matrix

Answer 6

When a 2x2 matrix is multiplied by the identity matrix which gives the original matrix

Question 7

How to work out the determinant

Answer 7

Det(a) = lead diagonal - bc
= ad - bc
A B
C D

Question 8

How to work out the inverse of A
A. B
C. D

Answer 8

Swap the lead diagonal and make the other 2 negative
D -B x 1/det(a)
-C A

Question 9

If the determinant of A = 0 what is A

Answer 9

Singular
So it doesn’t have an inverse matrix

Question 10

What is an inverse matrix

Answer 10

When a matrix is multiplied by its inverse it will equal the identity matrix which gives

Question 11

What is a transpose of a matrix

Answer 11

Rows become columns
Columns become row
A^t

Question 12

The transpose of a matrix of dimension m x n has dimension

Answer 12

Rows become columns
Columns become row
A^t

Question 13

What is a symmetric matrix

Answer 13

A = A^t
When a matrix is equal to its transpose

Question 14

How to work out the determinant of a 3x3 matrix

Answer 14

Switch the signs of each element going +,-,+,_
Pick an element and cross out the row and column that it is in and find the determinant of the left over numbers and times it by the first element

Question 15

How to find the minor of an element

Answer 15

Cross out the column and row of the element
Work out the discriminat

Question 16

What is the transformation matrix for a rotation of 90 degrees centre origin

Answer 16

0. -1
1. 0

Question 17

What is the transformation matrix for a rotation of 180 degrees centre origin

Answer 17

-1. 0
0. -1

Question 18

What is the transformation matrix for a rotation of 270 centre the origin

Answer 18

0. 1
   -1. 0

Question 19

What is the transformation matrix for a rotation of theta

Answer 19

CosX -sinX
SinX. CosX

Question 20

What is the transformation matrix for a reflection in the x-axis

Answer 20

1. 0
2. -1

Question 21

What transformation matrix for a reflection in the y-axis

Answer 21

-1. 0
0. 1

Question 22

What is the matrix transformation for a reflection in y=x

Answer 22

0. 1
1. 0

Question 23

What is the matrix transformation for a reflection in y=-x

Answer 23

0. -1
   -1. 0

Question 24

What’s the matrix transformation for an enlargement scale factor k

Answer 24

K. 0
0. K

Question 25

When u combine matrix transformations what do u do

Answer 25

Times them together

Question 26

In a transformation matrix, then the modulus of the determinant =

Answer 26

The area scale factor of the transformed shape A2 = |detA| x area A1

Question 27

How to solve simultaneous equations using matrices

Answer 27

A(x,y) = (16,-4) Times the answer by its inverse

Question 28

How to reverse the affect of a transformation

Answer 28

Multiply the image matrix by the inverse of the transformation matrix