How do you write the order of a matrix
The number of rows multiplied by the number of columns (e.g. 2 x 3)
What does a square matrix have
An equal number of rows and columns
What is the identity matrix
The identity matrix has diagonal 1s e.g. (1 0
It can be any size 0 1)
How do you determine if matrices can be multiplied?
Write the orders and if the middle numbers are equal it is possible. The outer numbers show the order of the answer
Commutative meaning
Multiplying things in any order gives the same answer, numbers are commutative but matrices are not
Associative
A(BC) = (AB)C= ABC and this is also true for matrices
Distributive
A(B+C)= AB + AC and this is also true for matrices
The multiplication of a matrix by the point (1,0) is equal to which column of a matrix
The first column
The multiplication of a matrix by the point (0,1) is equal to which column of a matrix
The second column
A stretch parallel to the x axis is transformed by what matrix
(K 0) By scale factor of K
(0 1)
A stretch parallel to the y axis is transformed by what matrix
(1 0) By scale factor of K
(0 K)
An enlargement by scale factor K is transformed by what matrix
(K 0)
(0 K)
A reflection in the x axis is created by what matrix
(1 0)
(0 -1)
A reflection in the y axis is created by what matrix
(-1 0)
(0 1)
A reflection in y=x is created by what matrix
(0 1)
(1 0)
A reflection in y=-x is created by what matrix
(0 -1)
(-1 0)
How do you find the determinant?
ad- bc
Are the points reversed or preserved if the determinant is negative?
The points are reversed
What method should you use for equations involving unknown coefficients or roots?
Use the equations for alpha, beta, gamma and delta
What method should you use for finding new roots with a relationship stated (e.g. 2alpha)
The substitution method where let w=2alpha so alpha=w/2 then swapping this into the equation
Relationships of roots in a quadratic
Relationships of roots in a cubic
Relationships of roots in a quartic
