1. Calculating the Determinant of a 3 by 3 Matrix NEXT This Concept tutor is a supplement to help you understand the process of calculating a determinant of a matrix. You will use a four step process. This Concept tutor is a supplement to help you understand the process of calculating a determinant of a matrix. You will use a four step process.

2. Applications of Matrices in Real-Life Used in real life applications (finance, science, manufacturing, optimizing, etc) to solve linear systems of equations. Delta Air Lines uses linear programming (based on matrix computations) to solve its flight scheduling problem. The problem is to match aircraft to flight legs and fill seats with paying passengers, there by reducing the operating cost.

3. Applications of Matrices in Real-Life Matrices are used with encryption in wi-fi communication. When you connect to a wi-fi hub in a restaurant, matrices and their inverses are used to encrypt your message.

4. Click here to watch the Introduction Click here to watch the Introduction NEXT Video on Introduction to a 3 x 3 matrix BACK

5. A = (1) What is a 32 in the Matrix A? NEXTBACK A) B) C) Select one of the following three options: Now it's your turn If you get the answer correct, you will go to master the next step. If you make a mistake, the system will take you to solve another problem.

6. B = (2) What is b 21 in the Matrix B? NEXTBACK A)B) C) Select one of the following three options: If you get the answer correct, you will go to master the next step. If you make a mistake, the system will take you to solve another problem. Now it's your turn

7. C = (3) What is c 23 in the Matrix C? NEXTBACK A)B) C) Select one of the following three options: Now it's your turn

8. Click here for the Definition video Part 1 Click here for the Definition video Part 1 NEXT Step 1: Definition of determinant and minor BACK

9. W = (4) What is the M 12 (minor row 1, column 2 ) ? BACK A) B)C) NEXT Now it's your turn Select one of the following three options:

10. Click here for the Definition video Part 2 Click here for the Definition video Part 2 NEXT Step 2: Applying Definition to a Matrix BACK

11. (-1) 1+3 *w 13 * |W| = (5) What is the 3 rd term in computing the Determinant W as shown below? (-1) 1+3 *w 13 * =(-1) 1+1 *w 11 * + (-1) 1+2 *w 12 * (-1) 2+3 *w 13 * BACK + ?? A) B) C) NEXT Select one of the following three options: Now it's your turn

12. Click here for the Definition video Part 3 Click here for the Definition video Part 3 NEXT Step 3: Solving the Minor of a Matrix BACK

13. d 11 d 12 |D| = d 21 d 22 | D |= (-1) 1+3 d 11 d 22 + (-1) 1+3 d 12 d 21 | D |= (-1) 1+2 d 11 d 21 + (-1) 1+1 d 12 d 22 | D |= (-1) 1+1 d 11 d 22 + (-1) 1+2 d 12 d 21 (6)What is the determinant of the 2 by 2 matrix D? BACK A) B) C) NEXT Now it's your turn Select one of the following three options: If you get the answer correct, you will go to master the next step. If you make a mistake, the system will take you to solve another problem.

14. -1 2 G = -2 1 (7) What is the determinant of a 2 by 2 matrix? 3 5 -5 BACK A) B) C) NEXT Select one of the following three options: Now it's your turn

15. Click here for the Definition video Part 4 Click here for the Definition video Part 4 NEXT Step 4: Final Step in Computing Determinant of a Matrix Step 4: Final Step in Computing Determinant of a Matrix BACK

16. Click here for the Example video Part 1 Click here for the Example video Part 1 Applying the Concept to Solving a Numerical Problem Step 1: First term of summation and Identifying the Minor Applying the Concept to Solving a Numerical Problem Step 1: First term of summation and Identifying the Minor BACKNEXT

17. A =A = (8) What is M 32 (minor 3, 2 ) in the Matrix A? A) B)C) BACKNEXT Select one of the following three options: Now it's your turn If you get the answer correct, you will go to master the next step. If you make a mistake, the system will take you to solve another problem.

18. B =B = (9) What is M 21 (minor row 2, column 1 ) in the Matrix B? A)B) C) BACKNEXT Now it's your turn Select one of the following three options: If you get the answer correct, you will go to master the next step. If you make a mistake, the system will take you to solve another problem.

19. C =C = (10) What is M 23 (minor row 2, column 3 ) in the Matrix C? A)B) C) BACKNEXT Now it's your turn Select one of the following three options:

20. Applying the Concept to Solving a Numerical Problem Step 2: Writing the Summation Equation Applying the Concept to Solving a Numerical Problem Step 2: Writing the Summation Equation BACKNEXT Click here for the Example video Part 2 Click here for the Example video Part 2

21. (-1) 1+3 *(1)* (11) What is the 3 rd term of summation of the determinant of W? (-1) 1+3 *(1)* (-1) 2+3 *(1)* BACK + ? A) B) C) NEXT = (-1) 1+1 *(2)* + (-1) 1+2 *(-4)* IWI = Now it's your turn Select one of the following three options:

22. Applying the Concept to Solving a Numerical Problem Step 3: Final solution Applying the Concept to Solving a Numerical Problem Step 3: Final solution BACKNEXT Click here for the Example video Part 3 Click here for the Example video Part 3

23. z =z = (12) Compute the determinant of the Matrix Z? A)B) C) BACK Now its your turn Select one of the following three options: -7085 -90

24. z =z = (12) Compute the determinant of the Matrix Z? A)B) C) Select one of the following three options: -7085 -90 The answer is incorrect! Check your calculations! Now its your turn BACK

25. z =z = (12) Compute the determinant of the Matrix Z? A)B) C) Select one of the following three options: -7085 -90 Congratulations! You understood the concept of calculating a determinant of a 3x3 matrix!