Matrix Notes - -- = - = +- = + 2 1 2 1 2 1 2 2 1 1 2 2 1 1...

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Unformatted text preview: -- = - = +- = + 2 1 2 1 2 1 2 2 1 1 2 2 1 1 c P P c c P P c P c P c ) 1 ( ) 1 ( ) ( ....... ........ .......... .......... .......... .......... .......... ....... ....... 2 1 2 1 2 1 2 22 21 1 21 11 3 3 2 2 1 1 2 2 3 23 2 22 1 21 1 1 3 13 2 12 1 11 = = + + + = + + + = + + + m n n m d d d x x x a a a a a a a a a d x a x a x a x a d x a x a x a x a d x a x a x a x a m n mn m m n n m n mn m m m n n n n d Ax = Elements of a matrix: ij a A is the coefficient matrix, x and d are known as vectors. A vector can be a row vector or a column vector. Both matrix and vectors have dimensions indicating to the number or rows and columns. For example, ( m x n) read m by n indicates that there are m rows and n columns. Remember, the row number always precedes the column number. Square matrix is a matrix that has equal number of rows and columns. = = 7 2 1 3 5 9 8 6 4 9 5 3 1 B or A Matrix operation- Addition, Subtraction and Scalar multiplication Two matrices A and B can be added with each other if and only if they have the same dimension. This is also true for matrix subtraction. This is known as conformability condition. We can multiply a matrix by a scalar. A scalar is a numerical element- a number. Null matrix and Identity Matrix: = = 1 1 1 I or A Properties of Identity Matrix = = = 3 2 1 1 1 2 1 v I A 1. AI=IA 2. AIB=AB 3. I 2 = I 3 =I; Any matrix with such a property is known as Idempotent matrix...
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This note was uploaded on 04/24/2011 for the course ECON 201 taught by Professor Takrimasyeda during the Fall '08 term at BRAC University.

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Matrix Notes - -- = - = +- = + 2 1 2 1 2 1 2 2 1 1 2 2 1 1...

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