What is the inverse of the matrix A given below? Some of the cofactors of A and the determinant of A have been computed for you.
Friday, March 19, 2010
Inverse of a Matrix
The inverse of a square non-singular matrix A is the matrix of cofactors of A divided by the determinant of A. A cofactor of an element of A is the determinant of the matrix which results from crossing out the row and column of A that contains the element, and which is then multiplied by -1 to the power of i+j, where i is the row and j is the column. Non-singular means that the determinant of A doesn't equal zero.
What is the inverse of the matrix A given below? Some of the cofactors of A and the determinant of A have been computed for you.
What is the inverse of the matrix A given below? Some of the cofactors of A and the determinant of A have been computed for you.
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The inverse of A is:
ReplyDelete(1 0 -2
0 1/5 0
-1 0 3)
Notice that the determinant of Inv(A) = 1/5, which is the reciprocal of the determinant of A.