Applying Cramer's rule on an nxn matrix

Question

Rune 2013-10-10

1
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回答： Ali Jadoon 2014-3-24

I need to find the solution to a system Ax=b using Cramer's rule. It needs to be Cramer's rule. I have made the following code that works for a 3x3 matrix, but i want it to work for an nxn matrix using a for-loop.

I can't figure out how to write the loop.

Thank you very much in advance!

n=3; d=10;

A = floor(d*rand(n,n)); b = randi(d,n,1);

D_A = det(A);

A_1 = A;

A_1(1) = b(1);

A_1(2) = b(2);

A_1(3) = b(3);

D_A_1 = det(A_1);

x1 = D_A_1/D_A;

A_2 = A;

A_2(4) = b(1);

A_2(5) = b(2);

A_2(6) = b(3);

D_A_2 = det(A_2);

x2 = D_A_2/D_A;

A_3 = A;

A_3(7) = b(1);

A_3(8) = b(2);

A_3(9) = b(3);

D_A_3 = det(A_3);

x3 = D_A_3/D_A;

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Answer 1

Roger Stafford 2013-10-10

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https://ww2.mathworks.cn/matlabcentral/answers/89800-applying-cramer-s-rule-on-an-nxn-matrix#answer_99241

编辑：Roger Stafford 2013-10-10

在 MATLAB Online 中打开

The two basic operations in applying Cramer's rule are: 1) replacing the k-th column of A by b and 2) obtaining the determinant of the various matrices which this produces, as well as the determinant of A. Hopefully you are allowed to use the matlab function 'det' for the latter purpose. The former one is accomplished in two steps by