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3 - ECMT 1020 SUMMER SCHOOL 09 LECTURE 3 MATRICES General...

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ECMT 1020 SUMMER SCHOOL 09 LECTURE 3 MATRICES
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General Approach- Matrices How should we approach this topic? It is not revolutionary mathematics but a systematic approach to handling multiple equations and related mathematical problems Although understanding of fundamental ideas is essential it also requires repetitive practice to master skills – thus completing exercise questions is extremely beneficial
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What is a Matrix? A matrix is a rectangular array of numbers Can be one-dimensional (vector) or two- dimensional. eg. a = [ 3 -1 5 ] b = 3 C = 2 8 3 5 5 1 7 4 9 8 0 2 6 The dimensions of a matrix are given in terms of (rows x columns) The dimensions of a are (1 x 3) and b has dimensions (2 x 1). Matrix C has dimensions (3 x 4)
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Other Types of Matrices Vectors are matrices of one dimension ( k x 1) or (1 x k) Square matrices are (k x k) D = 6 3 E = 2 4 1 2 5 4 5 0 7 6 6 Special square matrices are Identity matrices I 2 = 1 0 I 3 = 1 0 0 0 1 0 1 0 0 0 1
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Operations on Matrices Addition and Subtraction are fairly straight- forward with the only qualification being that matrices must be of the same dimension before these operations can be undertaken. (Matrices of different dimensions cannot be added) Multiplication is similar to scalar multiplication but the matrices must be compatible to qualify for multiplication. Division is not an operation that is applicable in matrix algebra
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Transposing a matrix Transposing a matrix is a useful tool in later applications. Transposing requires taking the rows of the matrix and making them the columns and the columns then become the rows. The transpose of A is usually denoted by A 4 2 A = 4 6 1 A ‘ = 6 0 2 0 7 1 7
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Addition and Subtraction Provided the matrices are of the same dimensions they can be added and subtracted. Addition of subtraction is on elements in identical positions in each matrix. F = 6 4 G = 2 2 F + G = 8 6 3 7 2 5 5 12 F = 6 4 G = 2 2 F - G = 4 2 3 7 2 5 1 2
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Multiplication In order to be multiplied matrices must be compatible . This means the number of columns in the first matrix must be identical to the number of rows in the
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