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Unformatted text preview: nolog matrix T, the solutio of this sy ng gy on ystem can be fo ound (appro oximately, b because of rounding) t be: to Now, just how did we get t d this inverted technolog matrix? Recall, from your d gy m ECO 211 clas that inver ON ss rting a 3 3 matrix is a simple a the follow as as wing rule: A1 = __1__ adj A A to nverse of th technolo matrix T he ogy T... So, t find the in we c find the cofactor m can matrix (we kn now that the determinant of T is n zero, so not o T is i invertible). The cofact matrix is tor s... 226 This, of course leads us to the adj T ( , o (i.e. row 1 b becomes co olumn 1, row 2 beco omes colum 2, and ro 3 becom column 3) as follow mn ow mes n ws: Now all we need to do is find the dete erminant of the techno f ology matrix to x comp plete the inversion! So let's do it o, t! member, from ECON 211, that the determina of a 3 3 matrix is as simple m e ant Rem as th following rule: he g or sim mply, A = a11a22a33 a11a23a32 + a12a23a3 a12a21a33 + a13a21a32 a13a22a31 3 31 2 For hnology ma atrix, the de eterminant w would be: which is simply a scalar! F our tech T= (0.8)(0.9) = )(0.8) (0.8 8)(0.2)(0.3 + (0.3)(0 3) 0.2)(0.1) (0.3)(0.4 4)(0.8) + (0.2)(0.4 4)(0.3) (0.2)(0.9)(0 0.1) T= 0.576 0.048 0.00 0.096 0.024 0 = 0 06 0.018 T= 0.384 = quired parts to get the matrix inve s ersion solution shown Now we have all of the req he age on th top of pa 226. 227 So, if the specif final dem f fic mand vector (say, the f r final output target of a deve elopment pr rogram) hap ppens to be e: in billions of dollars then the s s, follow wing specif solution v fic values will emerge fro our input output m om model (again in billions of dollars): s _ x1 = ___1___ [0 0.66 (10) + 0.30 (5) + 0 0.24 (6)] = 9.54 = 24.8 84 0.384 0.384 0 _ x2 = ___1___ [0 0.34 (10) + 0.62 (5) + 0 0.24 (6)] = 7.94 = 20.6 68 0.384 0.384 0 _ 0.21 (10) + 0.27 (5) + 0 0.60 (6)] = 7.05 = 18.3 36 x3 = ___1___ [0 0.384 0.384 An im mportant qu uestion now arises. Th producti of the o w he...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
 Spring '10
 sning
 Economics

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