Cramer's rule
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Definition
(advanced level)
If we have a system of linear equations which can be written Ax=b, then Cramer's rule can tell us how to find the components of x, as long as A is an invertible matrix.
Let D= - A - , the determinant of A.
Let A
1 be a matrix which is formed from A by replacing the 1st column with the vector b. Similarly let A
2 be a matrix which is formed from A by replacing the 2nd column with the vector b.
Now let D
1=|A
1|, the determinant of A
1, etc.
Then if we write x like (
), we have:
etc.
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