Matrix

Question 1

Inverse of a 2 x 2 matrix?

Answer 1

[ a b ] = 1/ det A [ d -b ]
[ c d ] = [ -c a ]

Question 2

How to know if there is an inverse to a matrix?

Answer 2

• Using Determinant of a Matrix
• If det A = 0 (inverse does not exist)
  -If det A is not 0 (inverse does exist)

Question 3

What if a matrix is SINGULAR?

Answer 3

det a = 0

Question 4

What if Matrix is NOT SINGULAR

Answer 4

det a does not equal 0

Question 5

How to work out det A

Answer 5

(A x D) - (B x C)

Question 6

How to double check an inverse of a matrix?

Answer 6

AA^-1 = I

Question 7

What are invariant lines?

Answer 7

Points which are mapped onto themselves

Question 8

What are some invariant lines?

Answer 8

-Mirror line
- Lines perpendicular to mirror line

Question 9

Invariant points?

Answer 9

Points in mirror line, which do not change

Question 10

When are there no invariant lines?

Answer 10

-In a rotation, theta does not equal 180 degrees

Question 11

When are there invariant lines in a rotation?

Answer 11

-When theta is equal to 180 degrees
-any line that passes through origin is invariant

Question 12

Matrix for reflection in y axis? (x=0) (DO)

Answer 12

( -1 0 )
( 0 1 )

Question 13

Matrix for reflection in x axis? (DO)

Answer 13

( 1 0 )
( 0 -1 )

Question 14

Matrix for reflection in x axis? (y=0) (DO)

Answer 14

( 1 0 )
( 0 -1 )

Question 15

Reflection in y=x (DO)

Answer 15

( 0 1 )
( 1 0 )

Question 16

Reflection in y=-x (DO)

Answer 16

( 0 -1 )
( -1 0 )

Question 17

How do you find the line invariant points of a matrix?

Answer 17

Matrix x (x) = (x)
(y) (y)

Question 18

How do you find invariant lines of a matrix?

Answer 18

Matrix x (x) = (x) then sub that into y = mx+c
(mx+c) (y)

TIP = for final answer always factor out x and c

Question 19

If you have a reflection that is y= x + 1 for etc? (DO)

Answer 19

Use translation for ( 1 0 0 )
( 0 1 -1 )
( 0 0 1 )

Question 20

Reflection for 3D? (DO)

Answer 20

x y z
( 1 0 0 ) make it -1 for what plane the question asks for
( 0 1 0 )
( 0 0 1 )