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How to find the inverse matrix

How to find the inverse matrix

Finding the inverse matrix requires the skills of dealing with matrices, in particular, the ability to calculate the determinant and transpose.

instructions

1

The inverse matrix is ​​obtained from the elements of the originalaccording to the formula: A ^ -1 = A * / detA, where A * - adjoint matrix, detA - determinant of the original matrix. The adjoint matrix - a matrix transpose amendments to the elements of the original matrix.

2

First get the determinant of the matrix, it isIt must be different from zero, as further determinant will be used as a divider. Suppose, for example, given a square matrix of the third order (consisting of three rows and three columns). As can be seen, the determinant of this matrix is ​​not zero, so there is an inverse matrix.

How to find the inverse & lt-strong & gt-matrix & lt- / strong & gt-

3

Search for add-ons to each element of the matrix A. Supplement to A [i, j] is the determinant of the submatrix obtained from the original by deleting the i-th row and j-th column, and this determinant is taken with the sign. The sign is determined by multiplying the determinant by (-1) in the degree of i + j. Thus, for example, in addition to A [2,1] is the determinant, discussed below. The sign was given as follows: (-1) ^ (2 + 1) = -1.

How to find the inverse & lt-strong & gt-matrix & lt- / strong & gt-

4

As a result, you get matrix ons now transpose it. Transposition - an operation which is symmetric about the main diagonal of the matrix, rows and columns are swapped. Thus, you find attached matrix A *.

How to find the inverse & lt-strong & gt-matrix & lt- / strong & gt-

5

Now divide each element by the determinant of the original matrix and get matrix the reverse of the original.

How to find the inverse & lt-strong & gt-matrix & lt- / strong & gt-

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