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Why Matrix Algebra. As more and more commodities are included in models, solution formulas become cumbersome.Matrix algebra enables to do us many things: provides a compact way of writing an equation systemleads to a way of testing the existence of a solution by evaluation of a determinantgives
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1. REVIEW OF: LINEAR MODELS AND MATRIX ALGEBRA From Chapter 4-5
Chiang and Wainwright, Fundamental Methods of Mathematical Economics
4th edition
2. Why Matrix Algebra As more and more commodities are included in models, solution formulas become cumbersome.
Matrix algebra enables to do us many things:
provides a compact way of writing an equation system
leads to a way of testing the existence of a solution by evaluation of a determinant
gives a method of finding solution (if it exists)
3. Catch Catch: matrix algebra is only applicable to linear equation systems.
However, some transformation can be done to obtain a linear relation.
y = axb
log y = log a + b log x
4. Matrices and Vectors Example of a system of linear equations:
c1P1 + c2P2 = -c0
?1P1 + ?2P2 = -?0
In general,
a11 x1 + a12 x2 ++ a1nXn = d1
a21 x1 + a22 x2 ++ a2nXn = d2
am1 x1 + am2 x2 ++ amnXn = dm
coefficients aij
variables x1, ,xn
constants d1, ,dm
5. Matrices as Arrays
6. Example: 6x1 + 3x2+ x3 = 22 x1 + 4x2+-2x3 =12 4x1 - x2 + 5x3 = 10