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
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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
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
