The document discusses matrix operations including addition, subtraction, and scalar multiplication of matrices. It provides examples of adding and subtracting matrices according to the rules of matrix arithmetic. The document also discusses solving matrix equations by setting matrix expressions equal to each other and solving the resulting systems of equations for the unknown values.

1. MATRICES 4.4C,D Norsyamimi Rosli Chong Pik Wei Bryan Shyeelan Fahmi

2. 4.4C Addition, Subtraction and Scalar Multiplication Learning outcome : You MUST know how to perform calculation on matrices involving addition (+), subtraction (-) and scalar multiplication (x) by the end of this presentation.

3. Introduction When we perform operations on matrices, the arithmetic rules must be followed . Example: Given; A= ( ) and B= ( ) Find: 3A + 2B -5 0 4 3 2 -1 6 2 3 1 -4 8

4. Solution: 3A + 2B = 3 ( ) + 2 ( ) = ( ) + ( ) = ( ) 6 3 3 1 -4 8 - 5 0 4 3 2 -1 18 6 9 3 -12 24 -10 0 8 6 4 -2 18 + (-10) 6 + 0 9 + 8 3 + 6 -12 + 4 24 + (-2)

5. = ( ) # Remember : B.O.D.M.A.S. (pg 107) 8 6 17 9 -8 22

6. Questions: Given: A= ( ) and B= ( ) Find: a) 2A + 3B – 2A b) 6B - 3A + 2A 2 5 9 3 2 4 19 1 14 8 2 7

7. 4.4D Solving Matrix Equations Learning outcome : You MUST know how to solve matrix equations involving addition (+), subtraction (-) and scalar multiplication (x) at the end of this presentation.

8. Introduction: With the knowledge of knowing how to find the values of unknowns, the same process will be used in this sub-topic. Example: If 3 ( ) - ( ) = ( ) , find the values of a, b, c and d. 3a -2 1 6b 4 2c 7d 1 2 6 -8 7

9. Solution: 3 ( ) - ( ) = ( ) ( ) - ( ) = ( ) ( ) = ( ) 3a -2 1 6b 4 2c 7d 1 2 6 -8 7 9a -6 3 18b 4 2c 7d 1 2 6 -8 7 9a – 4 -6 -2c 3 – 7d 18b -1 2 6 -8 7

10. So, 9a – 4 = 2 -6 – 2c = 6 9a = 2 + 4 - 2c =12 a = c =-6 3 – 7d = -8 18b – 1 = 7 -7d = -8 – 3 18b =7 + 1 -7d = -11 18b = 8 d = b = Therefore; a= , b= , c=-6 and d= .

11. Question: If 2 ( ) - 3 ( ) = ( ) , determine the matrix ( ) 13 9 7 a b c d 1 9 4 2 a b c d

12. End of Presentation… Thank you for you attention…