Matrices

Question 1

AB≠BA

Answer 1

Not commutative

Question 2

A(BC)=(AB)C

Answer 2

Associative

Question 3

What is the determinant of a 2x2 matrix?

Answer 3

ad-bc

Question 4

Whats the inverse for a 2x2 matrix?

Answer 4

d -b

-c a

Question 5

Whats the transformation matrix for a reflection in y axis?

Answer 5

-1 0

0 1

Question 6

Whats the transformation matrix for a reflection in x axis?

Answer 6

1 0

0 -1

Question 7

Whats the transformation matrix for a reflection in y=x?

Answer 7

0 1

1 0

Question 8

What does the determinant of a transformation matrix give?

Answer 8

Area scale factor

Question 9

What does a negative determinant of a transformation matrix mean?

Answer 9

Change of order to points

Question 10

(TS)^-1

Answer 10

S^-1 T^-1

Question 11

What is the formula for a general rotation?

Answer 11

formula booklet

Question 12

How do you work out a line of invariant points?

Answer 12

M(x,y)=(x,y)

Question 13

How do you work out an invariant line?

Answer 13

M(x,mx) = ? = (x’,y’)
Then substitute y=mx and solve for m

if +c then use y=mx+c and equate x terms and equate constant terms to solve for m and c

Question 14

Whats the transformation matrix for a reflection in x=0 3D?

Answer 14

Identity matrix but x=-1

Question 15

Whats the transformation matrix for a reflection in y=0 3D?

Answer 15

Identity matrix but y=-1

Question 16

Whats the transformation matrix for a reflection in z=0 3D?

Answer 16

Identity matrix but z=-1

Question 17

How do you find an eigen value?

Answer 17

|M-λI| = 0

Question 18

How do you find an eigen vector?

Answer 18

(M-λI)v=0

Question 19

What is U and D in M=UDU^-1?

Answer 19

D is eigen values as a diagonal matrix

U is eigen vectors

Question 20

Transformation R followed by S

Answer 20

SR