Matrices

Question 1

matrix for stretch parallel to x axis

Answer 1

m 0
0 1

1,0 maps to m,0

Question 2

matrix for stretch parallel to y axis

Answer 2

1 0
0 n

0,1 maps to 0,n

Question 3

matrix for shear w x axis fixed

Answer 3

1 k
0 1

0,1 maps to k,1 (x + ky)

Question 4

matrix for shear w y axis fixed

Answer 4

1 0
k 1

1,0 maps to 1,k (y + kx)

Question 5

If A then B is applied to x then what is the formula

Answer 5

y = BAx (first function closest to x)

Question 6

matrix for rotation x degrees anticlockwise around origin

Answer 6

cos x -sin x
sin x cos x

Question 7

a b
c d times by x y for a linear transformation

Answer 7

ax + by
cx +dy

Question 8

how to find the transformation of a matrix

Answer 8

apply changes to 1,0 and 0,1 then see what changed

Question 9

how to find the matrix for a transformation

Answer 9

apply changes to i 1,0 and j 0,1 then put new cords back in a matrix (i(two rows) j(two rows))

Question 10

matrix for enlargement sf k

Answer 10

k 0
0 k

Question 11

1 0
0 -1

Answer 11

reflection in x axis

Question 12

-1 0
0 1

Answer 12

reflection in the y axis

Question 13

0 1
1 0

Answer 13

reflection in y = x

Question 14

Reflection in y = -x

Answer 14

0 -1
-1 0

Question 15

matrices for 3x3

Answer 15

i 1,0,0 j 0,1,0 k 0,0,1 see where they map and draw columns with them - ijk

Question 16

reflection matrix 3 x 3

Answer 16

1 0 0
0 1 0
0 0 1

then replace a 1 with -1 based on reflection x y or z plane ( in order)

Question 17

3x3 matrix for rotation anticlockwise around x axis

Answer 17

1 0 0
0 cos x -sin x
0 sin x cos x

Question 18

3 x 3 matrix for anticlockwise rotation around y axis

Answer 18

cos 0 sin
0 1 0
-sin 0 cos

Question 19

3 x 3 matrix for anticlockwise rotation around z axis

Answer 19

cos -sin 0
sin cos 0
0 0 1

Question 20

how to find invariant points

Answer 20

map the transformation with x,y and use simultaneous equations to make x and y equal before and after

Question 21

how to find line of invariant points

Answer 21

map transformation with x, mx + c then use simultaneous equations and split x and c sides, make = 0 to find lines