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

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.

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.

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.