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Q&A #7255 |
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>Even though we think of a matrix being two dinensional, can it not be used >to represent 3 [x,y,z] equations with 3 unknowns which are talked about in >the 3rd dimension in college Calculus textbooks? Daniel, Matrices are used to solve 3 equations in 3 unknowns (x,y,z). I believe that although the equation may represent a situation in 3 dimensions, the way we set up the matrix does not. In fact matrices can be used to solve problems with 100 variables, although certainly not ones calculated by hand! As the number of variables and number of equations increase, the size of the matrix to represent them, also increases. My thought is that only two matrices are used to solve a system, no matter what size it is: the square one which contains the coefficients of the variables in the equations and the column matrix which contains the constants to which those equations are equal. The column matrix will always be of dimension n x 1, where n is the number of variables in the system. This is not a well-researched answer as the one Suzanne gave to your first question, just a "reasoned" one from what I know about solving systems using matrices. Hope it helps. -Kimberley, for the T2T service
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