Matracies

Question 1

What matrix represents a stretch in the x direction for 2x2 and 3x3?

Answer 1

K 0 0 K 0
0 1 0 0 1
0 0 1

Question 2

Stretch in the y direction for 2x2 and 3x3 matrices?

Answer 2

1 0 0 1 0
0 k 0 0 k
0 0 1

Question 3

Stretch in the Z direction for 3x3 matricies

Answer 3

1 0 0
0 1 0
0 0 k

Question 4

Enlargement with 2x2 and 3x3

Answer 4

K 0 0 K 0
0 k 0 0 k
0 0 k

Question 5

Reflection in x=0 for 2x2 ans 3x3 matrices?

Answer 5

-1 0 0 -1 0
0 1 0 0 1
0 0 1

Question 6

Reflection in y=0 for 2x2 and 3x3 matrices?

Answer 6

1 0 0 1 0
0 -1 0 0 -1
0 0 1

Question 7

Reflection in z=0 for 3x3 matrices?

Answer 7

1 0 0
0 1 0
0 0 -1

Question 8

Reflection in y=x for 2x2 and 3x3 matrices?

Answer 8

0 1 0 0 1
1 0 0 1 0
0 0 1

Question 9

General Rotation about the origin anticlockwise for 2x2 matrices?

Answer 9

Cosx -sinx
Sinx Cosx

Question 10

General rotation matrix about x axis

Answer 10

X= 1 0 0
0 cosx -sinx
0 sinx cosx

Question 11

General rotation matrix about y axis

Answer 11

Cosx 0 sinx
0 1 0
-Sinx 0 cosx1

Question 12

General rotation matrix about z axis

Answer 12

Cosx -sinx 0
Sinx cosx 0
0 0 1

Question 13

Det AB and detkA?

Answer 13

DetAB= detA x detB
DetkA= k^2 x detA

Question 14

Inverse of 2x2 matrix

Answer 14

1/ detM ( d -b)
(-c a)

Question 15

Inverse of 3x3

Answer 15

1/ detM ( matrix of cofactors which have been reflected in a line from top left to bottom right)

Question 16

How do you find eigen values?

Answer 16

M - lambder I | = quadratic, solve quadratic and they are your eigen values.

Question 17

How do you find eigen vectors?

Answer 17

|M - lambder I | v = 0
Sub eigen values into lambder, and get equations for x y z and put them in terms of t

Question 18

What does orthogonal mean?

Answer 18

Matrixa x matrixb = 0 and are perpendicular