Solving for Coefficients in Partial Fractions Example© 2001 by Karl Hahn |
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Here is the procedure for solving the linear equations in the example for A, B, and C by the method of Gaussian elimination. Each procedure tells you how to get from the current set of equations to the next set of equations.
| Equations | Procedure | |
A + B = 1
-2A + 2B + C = -2
A - 3B + 3C = 17
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Add 2 times first equation to second equation. Subtract first equation from third equation. | |
A + B = 1
4B + C = 0
-4B + 3C = 16
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Add second equation to third equation. | |
A + B = 1
4B + C = 0
4C = 16
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Subtract one quarter of the third equation from second equation. | |
A + B = 1
4B = -4
4C = 16
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Subtract one quarter of second equation from first equation. | |
A = 2
4B = -4
4C = 16
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Divide constants out of second and third equations to get solution. | |
A = 2
B = -1
C = 4
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Done. | |
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