The document discusses matrices and matrix operations. It provides examples of matrices with different orders (dimensions) and uses a 3x3 matrix to represent sales data of coffee, tea and soft drinks over three days. It also discusses properties and types of matrix operations like addition, subtraction, scalar multiplication and matrix multiplication.

1. Matrices

2. Matrices – How to write & What is Order 2 rows and 3 columns  Matrix has order 2x3 (read as “2 by 3”) 0.5 1 2 Shop 2 0.3 0.5 1 Shop 1 Pear Orange Apple

5. Matrices Observation 1: A + B = B + A  Addition is commutative Observation 2: (A + B) + C = A + (B + C)  Addition is associative

6. Matrices Scalar Multiplication: Matrix Multiplication: Remember: ROW multiply by COLUMN **Play this slide as slide show to view the multiplication step-by-step (3 × 3) + (4 × 1) = 13 (3 × 2) + (4 × 1) = 10 (1 × 2) + (3 × 1) = 5 (1 × 2) + (2 × 1) = 4

7. Matrices An electrical shop sold 5 televisions, 10 VCD players and 15 DVD players on Monday. On Tuesday, it sold 7 televisions, 8 VCD players and 9 DVD players. Given that the price of television is $90, the price of VCD player is $40 and the price of DVD player is $80, find the total sales for Monday and Tuesday. M T TV VCD DVD Total for Monday Total for Tuesday $T $V $D

8. Matrices

9. Matrices  Can only multiply matrices if these numbers are the same! B A  Not possible! (2 x 2) (3 x 2) Not equal!

10. Matrices Observation 1: Observation 2: (AB)C = A(BC)  Multiplication is associative AB = BA  Multiplication is NOT commutative!

11. Matrices The matrix with all entries zero is called a null matrix. This matrix is called the identity matrix . The diagonal are all 1’s. Observation 1: A0 = 0A = 0 Observation 2: AI = IA = A

13. Answer a = − 8, b = 238