How to solve by Kramer's method

How to solve by Kramer's method

Course of linear algebra and analytical geometry - basis of the higher technical education. ""Ruler"" comes to many students quite easily. Really, the main thing in linear algebra is to be able to solve the systems of the linear equations. The easiest way of calculation - Kramer's method.


1. For decisions systems of the equations by Kramer's method at first it is necessary to make an expanded matrix. In it square matrix has to consist of coefficients at variables, and a column of free members (expansion of a matrix) are free members from the right part of the equations.

2. We find determinant of the main matrix further. The most convenient way of finding of determinant - Gauss's method. Using elementary transformations, we try to obtain under the main diagonal of zero. Then the determinant is as the work of elements of the main diagonal. This determinant can be designated as D.

3. Further we carry out the following substitution - we change a column of a square matrix for a column of free members. Now we find determinant of this matrix. We designate it as DN where N is number of a column to the place of which substitution was made.

4. Now we find a solution of a system of the linear equations - we find equation roots. Xn = DN/D.

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