2. By: Prof. Y.P. Chiu1 Extra -2 Review of Linear Systems Extra -2 Review of Linear Systems Prof. Y. Peter Chiu By: Prof. Y. Peter Chiu 9 / 2011 9 / 2011

3. By: Prof. Y.P. Chiu2 §. L 23 : Cramer’s Rule A ‧ X = B X = B =

4. By: Prof. Y.P. Chiu3 X = A -1 B x i = §. L 23 : Cramer’s Rule

5. By: Prof. Y.P. Chiu4 Example 23-1 -2X 1 + 3X 2 - X 3 = 1 X 1 + 2X 2 - X 3 = 4 X 1 = -2X 1 - X 2 + X 3 = -3 B → X 1 = B →B → B

6. By: Prof. Y.P. Chiu5 §. L 24 : If ≠ 0 Then ① A -1 exist ② Linear System has nontrivial solution. ( 非 0 解 ) ③ rank A = n ④ The rows (columns) of A are linearly independent.

7. By: Prof. Y.P. Chiu6 §. L 26 : Gauss- Jordan reduction

8. By: Prof. Y.P. Chiu7 §. L 25 : Gaussian Elimination 高斯消去法 上三角 (upper triangular)

9. By: Prof. Y.P. Chiu8 §. L 27 : Homework ＃ 1 X 1 + X 2 + 2X 3 = -1 X 1 - 2X 2 + X 3 = -5 3X 1 + X 2 + X 3 = 3 (a) Using Gaussian Elimination method to find solution. (b) Using Gauss-Jordan reduction method. (c) Using Cramer’s rule ＃ 2 2X 1 + 4X 2 + 6X 3 = 2 X 1 + 2X 3 = 0 2X 1 + 3X 2 - X 3 = -5 Using Cramer’s rule to solve it.

10. By: Prof. Y.P. Chiu9 ＃ 3 Solve 3 X 1 - X 2 = 3 ＃ 4 Solve 2X 1 + X 2 +3X 3 = 2 X 1 + X 3 = 1 ＃ 5 Solve X 1 + 2X 2 +3X 3 = 6 4X 1 + X 3 = 4 2X 1 + 4X 2 +6X 3 = 11 §. L 27 : Homework

11. By: Prof. Y.P. Chiu10 The End