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Matrices, Rational equations, transformations

1

rotation matrix

cos0 -sin0

sin0 cos0

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2

reflection matrix

cos20 sin20

sin20 -cos20

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3

reflection over y = x

0 1

1 0

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4

rotation 90 degrees clockwise

0 1

-1 0

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5

matrix multiplication

row by column

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6

determinant of

a b

c d

ad - bc

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7

minor mij

the determinant formed by deleting row i and column j

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8

cofactor

cij = (-1)^i+j x mij (and apply sign rule)

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9

determinant of a inverse (^-1)

1/det(a)

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10

a matrix has an inverse if

the determinant does not equal 0

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11

det(ab)

det(a)xdet(b)

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12

a quadratic equation has no real roots if

b²-4ac<0

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13

transformation goes ____ the matrix

before

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14

composite

apply one then the other (r•g)

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15

translation matrix

1 0 h x

0 1 h x y

0 0 1 1

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16

rotate about point (h,k)

translate by (h, k), rotate, translate by (-h, -k)

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17

formula for inverse

1 d -b

/ x -c a

ad-bc

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18

point slope form

y - y1 = m(x - x1)

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