MATRICES - ECONOMETRIC THEORY Exercise 1(Tutorial Matrix...

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ECONOMETRIC THEORY: Exercise 1 (Tutorial) Matrix Algebra and Manpower Planning Matrix Multiplication in Microsoft Excel There is a limited set of matrix operations which may be performed in Excel with the use of predefined commands. The following commands are available in Version 4.0 : MMULT , MINVERSE , TRANSPOSE and MDETERM . In this exercise, we shall use only the first of these. For practice, we may multiply the matrices A = a 11 a 12 a 21 a 22 a 31 a 32 = 1 4 2 5 3 6 and b 11 b 12 b 13 b 21 b 22 b 23 = 7 9 11 8 10 12 to form the product AB = C = c 11 c 12 c 13 c 21 c 22 c 23 c 31 c 32 c 33 = 39 49 59 54 68 82 69 87 105 . To form the generic element c ij in the i th row and the j th column of C = AB , we take the elements of the i th row of A , which is a i. = [ a i 1 , a i 2 ], and we combine them with the elements of the j th column of B , which is b .j = [ b 1 j , b 2 j ] 0 , to give c ij = a i 1 b 1 j + a i 2 b 2 j . Notice that the j th column of B has been written as a row followed by a prime { 0 } which indicates that the row is to be transposed to form a column. We shall often employ this space-saving device for representing columns. Figure 1 shows the basic format and procedure for multiplying matrices. There are three steps: (i) Insert the elements of the matrices A and B in convenient arrays of cells. In the figure, the elements of A are in the range (B5:C7) and those of B are in the range (F5:H6). (ii) Select a output range in which the results are to be written. In the figure, the output range is (B11:D13).
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