How to find the inverse of a 2x2 matrix using gaussian elimination (not using rref or lu)?

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John Staine
John Staine 2018-5-18
评论： Jim Riggs 2018-5-18
Thanks

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回答（2 个）

Jim Riggs
Jim Riggs 2018-5-18
编辑：Jim Riggs 2018-5-18
The inverse of a 2x2 is very easy to calculate:
In terms of Matlab code:
detA = A(1,1)*A(2,2)-A(1,2)*A(2,1);
Ainv = (1/detA)*[A(2,2),-A(1,2);-A(2,1),A(1,1)];
(note that if detA is zero, the matrix has no inverse)
  2 个评论
Jim Riggs
Jim Riggs 2018-5-18
Gaussian elimination is not needed unless the matrix rank is greater than 3. For rank 2 and 3 there is a closed-form solution which is more efficient.

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the cyclist
the cyclist 2018-5-18
I found this answer by googling.

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