1. Dr. P. SHUM Email: EPShum@ntu.edu.sgEPShum@ntu.edu.sg Tel: 7904217 URL: http://www.ntu.edu.sg/home/epshum/education/ug.htm Dot Product

2. Dr. P. SHUM Email: EPShum@ntu.edu.sgEPShum@ntu.edu.sg Tel: 7904217 URL: http://www.ntu.edu.sg/home/epshum/education/ug.htm Cross Product

3. Dr. P. SHUM Email: EPShum@ntu.edu.sgEPShum@ntu.edu.sg Tel: 7904217 URL: http://www.ntu.edu.sg/home/epshum/education/ug.htm De Moivre’s Theorem DeMoivre's Theorem is true even if n is a complex number (has a real part and possibly an imaginary part), but when n is an integer we can prove the formula easily by using some basic trigonometry.

4. Dr. P. SHUM Email: EPShum@ntu.edu.sgEPShum@ntu.edu.sg Tel: 7904217 URL: http://www.ntu.edu.sg/home/epshum/education/ug.htm Determinant of a Matrix For a matrix A defined as Where C ij is the cofactor and k is an integer between 1 and n

5. Dr. P. SHUM Email: EPShum@ntu.edu.sgEPShum@ntu.edu.sg Tel: 7904217 URL: http://www.ntu.edu.sg/home/epshum/education/ug.htm Minor and Cofactor The minor, M ij, of the element a in a matrix A is the determinant of the matrix that remains after we delete the row i and column j containing a ij. The relationship between cofactor, C ij, and minor, M ij, is defined as follows:

6. Dr. P. SHUM Email: EPShum@ntu.edu.sgEPShum@ntu.edu.sg Tel: 7904217 URL: http://www.ntu.edu.sg/home/epshum/education/ug.htm Cramer’s Rule To solve a system of equations