ECON222 WEEK2 Matrices-1

ECON222 WEEK2 Matrices-1 - Lecture 6: Part 1 Topic:...

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1 1 Lecture 6: Part 1 Topic: Matrices Reading H&P, Ch 6 H&P, Ch 3, Sect 3.4. Reading for this lecture H&P, Ch 6, Sect 6.1. Homework for Tutorial in Week 3 Ex 6.1, pp. 231-232, problems 1, 3, 19, 23, 25. 2 A Matrix A matrix is a rectangular array of numbers. Example Input - output matrices show how the outputs of an economy’s industries are used by other industries and consumed as final demand. A B final demand manuf. 1000 500 1500 agric. 600 300 600 3 Matrices and Linear Equations The coefficients of a system of linear equations 5x + 2y – 3z – 0.1w = 10 ½x – 7y + 5.2z – 5.3w = -3 -9x + 0.3y – 2z + 4.1w = 0.5 can be written as matrices ⎡⎤ ⎢⎥ and ⎣⎦ 4 The Order of a Matrix The order of a matrix is “the number of rows by the number of columns”. Example The order of the following matrix 200 500 500 400 200 900 5 The Elements of a Matrix The numbers that comprise a matrix are called its elements. Example Any 2 x 3 matrix is written, in general, as: a 11 a 12 a 13 a 21 a 22 a 23
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ECON222 WEEK2 Matrices-1 - Lecture 6: Part 1 Topic:...

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