Inverse of a Matrix theory

Inverse of a Matrix

Definition method.

If the product between two matrices is the identity matrix, then we say that the matrices are “inverse”; because by multiplying them we obtain the neutral element for the product .

Consider the inverse matrix:

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It must accomplish that: A · A^-1 = I

Observe the following example.

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So, we obtain the following equations system to get the inverse matrix values.

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Determinant method.

By applying this method we say that:

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Where att (A)^t is attached matrix and det (A) is the determinant of the matrix A.

The A determinant solution can be seen in the corresponding section about determinants theory.

att (A)^t is obtained as follows:

Given matrix A:

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Its attached is formed by the determinings which are result by suppressing a row and column of each of one of the elements.

For example, the a₃₂ element position would be occupied by the determining which results by eliminating the third row and second column, that is:

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and as the row + column (3+2) is odd we change the sign.

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Then we perform its transpose:

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You can download the App BioProfe READER to practice this theory with self-corrected exercises.