Karteikarten
FP1 notes
Karten in diesem Stapel (9)
- 1Matrices - numbers in cells are elements. Order of matrix is rows x columnsThey are incompatible if you add or subtract matrices with different orders.
Each element is +/- to the one in the other matrix - 2Transformations - Can describe the transformations as a pair of equations x' = ax + cy y' = bx + dy summarise into matrix (a c) (b d)Reflection in the line y = x
matrix is (0 1)
(1 0) - 3Rotation through angle anticlockwise about the origin; (cos@ -sin@) (sin@ cos@)Rotation through angle clockwise about origin;
( - 4Multiplying matrices co ordinates (x,y) can be written as a column vector; (x) (y)You times he row of first matrix with each column in the second matrix.
In order to multiply he columns of first and rows of second must equate. - 5Multiplication is not commutative Product AB does not equal Product BA. Sometimes alternative product does not exist.Multiplication is associative
(PQ)R = P(QR) - 6identity matrix is (1 0) (0 1) doesn't change matrixComposition of transformations
Two transformations X then Q on an object. The single composite transformation is QX. - 7Inverse matrices - M x M' = Identity matrix M' = 1/d (d -c) (-b a) provided that d is not zero.The determinant of a 2 x 2 matrix is ad - bc.
No inverse if det = 0 and is singular
Inverse if det # 0 and is non -singular - 8Inverse of a product - (AB)' = B'A' To undo a transformation you must undo the second transformation before the first.If det T = 0 it is singular, transformation by T maps every point in the plane on to a single line through the origin.
- 9Finding the equation of the straight line mapped - 4x - 6y = 6 2x - 3y =s
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- Karteikarten am FP1 notes, erstellt von chubecka am 07/11/2013.
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- chubecka
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