(New page: Cramer's Rule can be used to solve a system of linear equations: Given a system of linear equations A*x=b where A is an invertible square matrix, the theorem says that <math><img class="t...) |
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Cramer's Rule can be used to solve a system of linear equations: | Cramer's Rule can be used to solve a system of linear equations: | ||
| − | Given a system of linear equations A*x=b where A is an invertible square matrix, the theorem says that <math> | + | Given a system of linear equations A*x=b where A is an invertible square matrix, the theorem says that <math>x_i = \frac{\det(A_i)}{\det(A)} \qquad i = 1, \ldots, n \, " src="http://upload.wikimedia.org/math/f/7/7/f772877984cbae5c47877d4ced245b6c.png</math>, where Ai is a matrix formed by replacing the ith column of A with the vector b. |
Revision as of 13:50, 19 January 2009
Cramer's Rule can be used to solve a system of linear equations:
Given a system of linear equations A*x=b where A is an invertible square matrix, the theorem says that $ x_i = \frac{\det(A_i)}{\det(A)} \qquad i = 1, \ldots, n \, " src="http://upload.wikimedia.org/math/f/7/7/f772877984cbae5c47877d4ced245b6c.png $, where Ai is a matrix formed by replacing the ith column of A with the vector b.
