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Matrices

Matrices. What you need to learn. Know how to write a Matrix Know what is ORDER of Matrices Addition and Subtraction of Matrices Multiplication of Matrices Using Matrices to solve simultaneous equations (Find determinant, Inverse) Using Matrices to solve word problems. Resources.

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Matrices

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  1. Matrices

  2. What you need to learn • Know how to write a Matrix • Know what is ORDER of Matrices • Addition and Subtraction of Matrices • Multiplication of Matrices • Using Matrices to solve simultaneous equations (Find determinant, Inverse) • Using Matrices to solve word problems

  3. Resources • Textbook Ch 1 (Section 1.3) – for Solving simultaneous equations • Notes in this powerpoint • Other notes and worksheets attached

  4. Matrices – How to write & What is Order 2 rows and 3 columns  Matrix has order 2x3 (read as “2 by 3”)

  5. C T SD M T W Matrices E.g: A drink stalls sold 160 cups of coffee, 125 cups of tea and 210 glasses of soft drinks on Monday. On Tuesday, it sold 145 cups of coffee, 130 cups of tea and 275 glasses of soft drinks. On Wednesday, it sold 120 cups of tea, 155 cups of coffee and 325 glasses of soft drinks. Design a matrix to represent this information. State the order of your matrix. OR order 3x3

  6. Matrices • Matrix Operations B – A ? Observation 1: Matrices must be same order to add or subtract

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

  8. (3 × 2) + (4 × 1) = 10 (3 × 3) + (4 × 1) = 13 (1 × 2) + (2 × 1) = 4 (1 × 2) + (3 × 1) = 5 Play as slide show Matrices Scalar Multiplication: Remember: ROW multiply by COLUMN Matrix Multiplication:

  9. TV VCD DVD $T $V $D Total for Monday M T Total for Tuesday 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.

  10. Matrices

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

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

  13. 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

  14. *Inverse Matrices* The inverse of the matrix A = is given by,  Determinant of A

  15. *Inverse Matrices*

  16. Practice • Find • (a) BA • (b) BA – 2A • If , find a and b.

  17. Answer a = − 8, b = 238

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