Matrices

Question 1

What is a matrix?

Answer 1

A table of values

Question 2

What is meant by the order of a matrix?

Answer 2

The number of rows and columns.

Question 3

When determining the order of a matrix, are the rows or columns looked at first?

Answer 3

Rows, then columns

Question 4

What is an element in a matrix?

Answer 4

An individual term

Question 5

What is a square matrix?

Answer 5

Matrices with the same number of rows and columns (2x2, 3x3, 4x4, etc)

Question 6

What is meant by matrices being non-conformable under addition?

Answer 6

You can’t add or subtract matrices of different orders

Question 7

How do you multiply a matrix by a scalar?

Answer 7

Multiply each element within the matrix by the scalar

Question 8

What is the identity matrix?

Answer 8

A matrix with 1 down the diagonal and the rest 0

Question 9

What is meant by associativity?

Answer 9

(xy) * z = x * (yz)

Question 10

What is meant by commutativity?

Answer 10

xy = yx

Question 11

Is matrix addition associative?

Answer 11

Yes

Question 12

Is matrix subtraction associative?

Answer 12

No

Question 13

Is matrix addition commutative?

Answer 13

Yes

Question 14

Is matrix subtraction commutative?

Answer 14

No

Question 15

Is matrix multiplication commutative?

Answer 15

No

Question 16

In order to multiply 2 matrices, what must the form be?

Answer 16

( a x n) x (n x b)

Question 17

What order will the resulting matrix of ( a x n) x (n x b) be?

Answer 17

a x b

Question 18

Is matrix multiplication associative?

Answer 18

Yes

Question 19

What is meant by matrix multiplication being distributive?

Answer 19

A(B+C) = AB+AC

Question 20

What is the general form for a rotation transformation matrix?

Answer 20

(cos x -sin x)
(sin x cos x)`

Question 21

What is a shear?

Answer 21

Each point in one axis is moved by a multiple of its other axis

Question 22

What is the general matrix for a shear parallel to the x-axis?

Answer 22

(1 a)
(0 1)

Question 23

What is the general matrix for a shear parallel to the y-axis?

Answer 23

(1 0)
(b 1)

Question 24

How would you describe a shear?

Answer 24

A shear of factor z, x/y-axis invariant, where the point (a,b) is mapped to (c,d)

Question 25

How do you combine matrix transformations?

Answer 25

Transformation A followed by transformation B is the same as applying BA

Question 26

How would you find invariant points with matrices?

Answer 26

Put it in the form: (a b)(x) = (x)
(c d)(y) = (y)
Then form equations and simplify