Section 1: Introduction to Matrices
1. Check answers carefully :
2. Make sure you are familiar with the matrices for simple transformations :
Know the matrices for :
Reflection in x & y axis and lines y=x & x=y
Rotation through 90 or 180 degrees about origin.
3. Also become familia with matrices for enlargement and two-way stretches :
Numbers are on leading diagonal and zeros on the other positions.
4. Know the general rotation matrix :
Matrix for rotation of O anticlockwisw about origin.
cos O - sin O
sin O cos O
5. Remember useful result about the columns of a matrix :
Image point (1,0) gives first column
Image point (0,1) gives second column
Section 2: Matrix Multiplication
1. Make sure you can do matrix multiplication confidently :
2. Remember matrix multiplication is not commutative :
General AB does not = BA
3. Make sure matrices are in the correct order for composite transformations :
Remember transformation A follwed by B represent BA matrix.
Section 3: Inverse Matrices
1. Remember rule for the inverse matrix product :
For square matrices M and N, (MN)-1 = N-1 M-1.
2. Make sure you understand the significance of a zero determinant for a matrix transformation :
For matrix with zero determinant all points are mapped onto a straight line.
3. Remeber the physical significance of the determinant :
Determinant of matrix represents the area of scale factor of the associated transformation. Area scale factor is the square of the scale factor.
Section 4: Matrices and simultaneous equations
1. Be careful when solving matrix equations for which the matrix has no inverse :
Can mean either no solution or infinitely many solutions.
2. Remember that the origin is always an invarient point for a linear transformation :
3. Make sure that you know the difference between a line of invarient points and invarient line :
Invarient point is mapped to itself.
Invarient line is a line of points each mapped to itself.