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Brief proof of the Cramer method




In the English version of the site, I saw a brief proof of the ruler of the crater and I could not understand it. Please give advice – what does the author mean? Thanks

Answer 1, Authority 100%

In general, see here , for example.

And so – everything is simple. So, there is a source system

artificially expand vectors (x, y) and (p, q) to the matrices shown:

As we see, the equations themselves have not changed, and the addition of (0 1) and (B d) led to the identity, so that we did not add anything new (no new roots, nor new conditions on the roots).

Next, since the determinant of the work of the matrices is equal to the product of the determinants, as well as simply finding the distributor of an extended matrix, which is just X , we find that

Where exactly do you get x as the ratio of two determinants.

For Y all the same, only an extended matrix has the kind of

That’s all.

Answer 2, Authority 100%

  1. by the property of the determinant DET (AB) = DET (A) DET (B)
  2. Det ([x, 0] [y, 1]) = x * 1-y * 0 = x
  3. dx = d1 = & gt; x = d1 / d

The author translates the column vector (x, y) into the matrix to use the property of the determinant.

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