ECON222 WEEK3 -LECTURE9-1(HW WEEK5)

ECON222 WEEK3 -LECTURE9-1(HW WEEK5) - Lecture 9 Topic...

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1 Lecture 9: Topic: Matrices Reading for this lecture H&P, Ch 6, Sect 6.6 pp. 138 – 148 Homework for Tutorial Week 5 Ex 6.6, pp 269 – 270 problems 1, 5, 9, 21, 27 The Inverse of a 3 x 3 matrix A = 33 32 31 23 22 21 13 12 11 a a a a a a a a a The determinant of a 3 x 3 matrix - Expanding by the first row gives A = a 11 33 32 23 22 a a a a - a 12 33 31 23 21 a a a a + a 13 32 31 22 21 a a a a a 11 (a 22 a 33 – a 32 a 23 ) – a 12 (a 21 a 33 – a 31 a 23 ) + a 13 (a 21 a 32 – a 31 a 22 ) Minors and Cofactors 33 32 23 22 a a a a is the minor of a 11 33 31 23 21 a a a a is the minor of a 12 32 31 22 21 a a a a is the minor of a 13
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2 A minor with the prescribed sign attached to it is called a cofactor. The cofactor of a 11 is 33 32 23 22 a a a a The cofactor of a 12 is - 33 31 23 21 a a a a Eg: A = 7 6 9 8 1 3 5 2 4 A = 4(7 – 48) – 2(21 – 72) + 5 (18 – 9) = -17 the cofactor matrix is C = 1 3 2 4 8 3 5 4 8 1
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ECON222 WEEK3 -LECTURE9-1(HW WEEK5) - Lecture 9 Topic...

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