Year 1 Further Pure Flashcards
(3x2)
3 rows (down)
2 columns (across)
Commutative
AB = BA
Associative
(AB)C = A(BC)
Distributive
A(B+C) = AB + AC
(A+B)C = AC + BC
Is a matrix commutative, associative and distributive
A matrix is not commutative but is associative and distributive
Invariant point
A point mapped to itself by a transformation
Invariant line
A point on a line which is mapped to another point on the line
Argand diagram
Y axis = complex numbers
X axis = real numbers
Sum of roots
-b/a
n Sigma r (r)
1/2n (n+1)
n Sigma r (r^2)
1/6n (n+1)(2n+1)
n Sigma r (r^3)
1/4 n^2 (n+1)^2
Singular matrix
Det = 0
Determinant
The scale factor of enlargement during a transformation
Consistent equation
Infinitely many solutions
Inconsistent equation
No solutions
Three planes on top of each other
Three parallel
Two planes on top of each other on not
Two parallel one not
Triangular prism
Det = 0
Inconsistent equation
Sheeth
Det = 0
Consistent equation
Unique solution
Determinant != 0
Dot product equation
Length of a x length of b x cos (theta) = a.b
a.b = 0
Orthogonal
r.n = a.n
General point . Normal = position vector . Normal
