Precalc Unit 6

Matrices, Rational equations, transformations

rotation matrix

rotation matrix

cos0 -sin0

sin0 cos0

reflection matrix

cos20 sin20

sin20 -cos20

reflection over y = x

0 1

1 0

rotation 90 degrees clockwise

0 1

-1 0

matrix multiplication

row by column

determinant of

a b

c d

ad - bc

minor mij

the determinant formed by deleting row i and column j

cofactor

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

determinant of a inverse (^-1)

1/det(a)

a matrix has an inverse if

the determinant does not equal 0

det(ab)

det(a)xdet(b)

a quadratic equation has no real roots if

b²-4ac<0

transformation goes ____ the matrix

before

composite

apply one then the other (r•g)

translation matrix

1 0 h x

0 1 h x y

0 0 1 1

rotate about point (h,k)

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

formula for inverse

1 d -b

/ x -c a

ad-bc

point slope form

y - y1 = m(x - x1)