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©1998 ThinkQuest
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©1998 ThinkQuest
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Appendix: Discrete Algebra
When comes to finding the inverse of a matrix, the concept of determinant is very important. A determinant is a real number represented by a square array of numbers. The determinant can be acquired by cross-multiply and then subtract the first few results from the last few results. The ways of finding the inverse of matrices are different for 3x3 and up matrices than 2x2 matrices. To find the inverse for 2x2 matrices, exchange the first number in the first row with the second number in the second row, and multiply the second number in the first row and the first number in the second row with –1. After that, multiply each resulting number with 1/the determinant of the matrices. To find the inverse for 3x3 and up matrices, exchange the rows with the columns. Then multiply every other number starting the second number in a matrix by –1. Finally, multiply every resulting number by 1/the determinant of the matrices. (Note: if the determinant is zero, there is no inverse).
The most useful ways to use matrices is that to solve systems of equations. You can do this by putting all the coefficients of the variables in the form of matrices. Then you manipulate the matrices by adding or subtracting the row from the other row so that you can get the last row of the matrices with only one non-zero number, and the every row upward has one more non-zero number than the row below. Finally, plug in the last row into its corresponding equation to solve its only variable. Then use the solved the variable to solve the additional equations in the systems.
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