discuss on how to solve determinants in mathematics

for educational purposes only

1. GOOD MORNING CLASS!

2. Instructions: Cross out words that consists of three or four letters. Cross out words that consists of six letters. Cross out words that consists of ten or eleven letters. Cross out words that consists of fourteen or more letters. Permutation Matrix Odd Inversions N Factorial Triangular form Even Determinants ENGAGE: WORD REMOVAL (3 MINUTES)

3. Based on our activity. What does the hidden word tell us? In your own words, how can you define the word that you have answered in number 1? Explain the importance of determinants. Follow up questions:

4. DETERMINANTS

5. At the end of the lesson, the students will be able to: Use the properties of determinants to solve problems. Solve determinant. Solve determinant via reduction to triangular form. Explain the importance of determinants. OBJECTIVES

6. Criteria: Complete solutions ------- 50% Clearly and detailed explanations ---- 50% Total --------------------------- 100% SOLVE ME! (group activity) Allotted time: 10 minutes

7. 1 2 3 4

8. SOLUTIONS! Question #1 Solution Solve the determinant of 2x2 matrix. 2 -3 A= 4 5 A= a₁₁ a₁₂ a₂₁ a₂₂ To obtain det (A) we write down the terms a ₁ - a₂ - and a₁ - a₂ - Fill in the blanks with all possible elements of S₂; the subscript becomes 12 and 21. Since 12 is an even permutation, the term a₁₁ a₂₂ has a negative sign associated with it. Hence det (A) = a₁₁a₂₂ - a₁₂a₂₁

9. We can also obtain det (A) by forming the product of the entries on the line from left to right in the following diagram and subtracting from this number the product of the entries on the line from right to left. Thus, A = 2 -3 4 5 Then, det (A) = (2) (5) – (-3)(4) = 10 – (-12) = 10 + 12 = 22.

10. A = Solution : A= Then, to compute det (A), we write down six terms And 2. Solve the determinant of a 3x3 matrix

11. All the elements of S ₃ are used to fill in the blanks, and if we prefix each term by + or by – according to weather the permutation used is even or odd, we find that

12. 3. If det (A) = 2, det (B) = 3, and the size of A and that of B is 2 x 2, find the value of det (2A) + det (3B) + det (AB) using the properties of determinants. Solution:

13. 4. Evaluate the given determinant via reduction to triangular form.

14. Follow up questions What method did you use in solving determinants? Was the activities helpful in solving determinants? In what way was the activities helpful in solving determinants?

15. Definition of Determinant Determinant is a number associated with the square matrix. To every square matrix A = of order n, we can associate a number (real or complex) called determinant of the square matrix A. Determinant of matrix [A] is donated by Please Be with Me

16. I Found You (individual activity) 8 minutes

17. PLEASE CHOOSE ME! (5minutes)

18. ANSWER KEY!!! C A B D B

19. Give one example in each properties of determinants with complete solutions. ( 40 points) ASSIGNMENT: “I AM LOOKING WITH YOU”

20. THANK YOU AND GOD BLESS!