ECON222 WEEK3 -LECTURE8

ECON222 WEEK3 -LECTURE8 - Lecture 8: Topic: Matrices...

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1 Lecture 8: Topic: Matrices Reading for this lecture H&P, Ch 3, Sect 3.4 pp. 138 – 148 H& P, Ch 6, Sect 6.4, 6.5, 6.6 pp. 249 – 259 Homework for Tutorial Week 4 Ex 3.4, pp 146 – 148 problems 1, 15 Matrix Inversion The inverse of a matrix, A, denoted by A -1 , is defined only if A is a square matrix and it is non-singular . If the determinant of A is non-zero, A 0, then it is non- singular. If A = 0 then it is singular. The determinant of a 2 x 2 matrix ab A cd ⎡⎤ = ⎢⎥ ⎣⎦ is A ad bc =− The inverse of A can be calculated: A -1 = 1 Adj A A Some Definitions: Adjoint A is the transpose of the cofactor matrix. A cofactor matrix is a minor with the prescribed sign attached to it. Minor: that part of the matrix that remains when the row and column to which the element belongs is removed.
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2 Example: The Inverse of a 2x2 Matrix A = 2 1 4 6 A = 6(2) – 4(1) = 8 A 0 therefore it is non-singular. Finding the cofactor matrix to get the adjoint C = 6 4 1 2 Adj A = C T =
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ECON222 WEEK3 -LECTURE8 - Lecture 8: Topic: Matrices...

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