Matrices

Question 1

How do you write the dimensions of a matrix?

Answer 1

Row X Column

Question 2

What is a square matrix?

Answer 2

A matrix is a square if it has the same number of rows as columns

Question 3

What is a zero matrix?

Answer 3

A zero matrix is one in which all the elements are 0

Question 4

What is an identity matrix?

Answer 4

An identity matrix is a square matrix which as 1’s In the ‘leading diagonal’ and 0 elsewhere

Question 5

What the properties of matrix multiplication?

Answer 5

Matrix multiplication is associative but not commutative

Question 6

What dictates for two matrices can be multiplied?

Answer 6

They multiply if P x Q *** Q x P

Question 7

What type of matrices can be raised to a power?

Answer 7

Square Matrices

Question 8

What is a linear transformation?

Answer 8

T(ka) = kT(x)
(kb) (y)

T(a + b) = T(a) + T(b)

Question 9

What does i- and j- represent?

Answer 9

i- = (1) and j- = (0)
(0) (1)

Question 10

How could a matrix transformation be represented in terms of i- and j-?

Answer 10

( T[i] T[j] )

Where ‘T’ is the transformation of ‘I’ and ‘j’

Question 11

What matrix represents an enlargement of SF ‘k’?

Answer 11

(k 0)
(0 k)

Question 12

What matrix represents a rotation of ‘x’ anticlockwise?

Answer 12

(cos x -sinx)
( )
(sin x cosx)

This is an ANTICLOCKWISE rotation

Question 13

What is a shear transformation?

Answer 13

A shear transformation is when one direction is changed and the other stays the same

Question 14

What is the matrix for a stretch of scale factor ‘k’ parallel to the x axis?

Answer 14

(k 0)
(0 1)

Question 15

What is the matrix for a stretch of scale factor ‘k’ parallel to the y axis?

Answer 15

(1 0)
(0 k)

Question 16

What is the matrix for a shear with a fixed x axis?

Answer 16

(1 k)
(0 1)

Question 17

What is the matrix for a shear with a fixed y axis?

Answer 17

(1 0)
(k 1)

Question 18

What is the formula for the shear factor?

Answer 18

Distance between a point and its image///Distance between original point and x-axis = SF

Question 19

How do you calculate the combined transformation for B and then A?

Answer 19

Matrix A *** Matrix B

It is always the second one multiplied by the first one

Question 20

What are the dimensions of the matrix for 3D transformations?

Answer 20

3x3

Question 21

What do i-, j-, and k- equal?

Answer 21

i* = (1) j* = (0) k* = (0)
(0) (1) (0)
(0) (0) (1)

Question 22

What is the matrix for a reflection in the plan z = 0?

Answer 22

(1 0 0)
(0 1 0)
(0 0 -1)

Question 23

What is the matrix for a reflection in the plan x = 0?

Answer 23

(-1 0 0)
(0 1 0)
(0 0 1)

Question 24

What is the matrix for a reflection in the plan y = 0?

Answer 24

(1 0 0)
(0 -1 0)
(0 0 1)

Question 25

What is the matrix for a rotation ‘x’ degrees anticlockwise about the y axis?

Answer 25

(cosx 0 sinx)
(0 1 0)
(-sinx 0 cosx)

Question 26

What is the matrix for a rotation ‘x’ degrees anticlockwise about the x axis?

Answer 26

(1 0 0)
(0 cosx -sinx)
(0 sinx cosx)

Question 27

What is the matrix for a rotation ‘x’ degrees anticlockwise about the z axis?

Answer 27

(cosx -sinx 0)
(sinx cosx 0)
(0 0 1)