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You are not logged in. #1 20100712 04:50:13
Inverse of square matrixIf you take the square matrix: It's inverse is Doesn't sound very interesting! What about this? consider this matrix Now if means the rth row and cth column element. now delete the rth row and cth column to make a n1 X n1 matrix find it's determinent and call it in the below matrix is represented by form the matrix (the plus/minus sign is becuase you need to know the size of the matrix to know the sign of the bottom row) In words what has been done: change lowercase to capital (or from E to D) start with the outer two elements which form diagonals swap the elements round (there's only one element in each so nothing changes) go to the next diagonal pair (one inwards on either side) and swap them (the elements within the diagonal see above) and keep going also the sign of the outermost diagonals stay the same the next pair change sign, whether the trailing diagonal (what all these diagonals are parallel to) changes depends on the size. Calculate the determinent Δ in the following way: (multiply the first row of original matrix by the first column of the new matrix) To find the detiminent of the n1 X n1 matrices use the above method (which means looking at n2 X n2 matrices and so on down to 2 X 2 whose determinent is above if you put say that the determinent of a 1 X 1 matrix is its one element (which means the method above dosen't work on 1 X 1) then for the 2 X 2: then right: and sustitute which fits the above using this method you can find the inverse of a n X n matrix provided you know how to do the n1 X n1 (you just have to work your way backwards to the 2 X 2 unfortunatly I don't know how to prove it! Why did the chicken cross the Mobius Band? To get to the other ...um...!!! #2 20100726 12:58:51
Re: Inverse of square matrixDeterminant is created to solve equations using the Crammer's Rule. X'(yXβ)=0 #3 20100726 22:03:31
Re: Inverse of square matrix
I don't understand what you mean. I don't know if I've actually achieved anything yet Why did the chicken cross the Mobius Band? To get to the other ...um...!!! #4 20100727 16:27:05
Re: Inverse of square matrixsorry for the typo Cramer mistaken as Crammer X'(yXβ)=0 