Matrices Flashcards
matrix for stretch parallel to x axis
m 0
0 1
1,0 maps to m,0
matrix for stretch parallel to y axis
1 0
0 n
0,1 maps to 0,n
matrix for shear w x axis fixed
1 k
0 1
0,1 maps to k,1 (x + ky)
matrix for shear w y axis fixed
1 0
k 1
1,0 maps to 1,k (y + kx)
If A then B is applied to x then what is the formula
y = BAx (first function closest to x)
matrix for rotation x degrees anticlockwise around origin
cos x -sin x
sin x cos x
a b
c d times by x y for a linear transformation
ax + by
cx +dy
how to find the transformation of a matrix
apply changes to 1,0 and 0,1 then see what changed
how to find the matrix for a transformation
apply changes to i 1,0 and j 0,1 then put new cords back in a matrix (i(two rows) j(two rows))
matrix for enlargement sf k
k 0
0 k
1 0
0 -1
reflection in x axis
-1 0
0 1
reflection in the y axis
0 1
1 0
reflection in y = x
Reflection in y = -x
0 -1
-1 0
matrices for 3x3
i 1,0,0 j 0,1,0 k 0,0,1 see where they map and draw columns with them - ijk
reflection matrix 3 x 3
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)
3x3 matrix for rotation anticlockwise around x axis
1 0 0
0 cos x -sin x
0 sin x cos x
3 x 3 matrix for anticlockwise rotation around y axis
cos 0 sin
0 1 0
-sin 0 cos
3 x 3 matrix for anticlockwise rotation around z axis
cos -sin 0
sin cos 0
0 0 1
how to find invariant points
map the transformation with x,y and use simultaneous equations to make x and y equal before and after
how to find line of invariant points
map transformation with x, mx + c then use simultaneous equations and split x and c sides, make = 0 to find lines
