Matrix method

Definition 4.1: A square matrix

is said to be invertible if there exists a matrix such that , where is the identity matrix. A matrix is called inverse of.

Theorem 4.2: A matrix is invertible if and only if has nonzero determinant.

The formula of inverse matrix ofis:

=,

were , – transposed matrix of cofactors of matrix .

Let to rewrite system in a matrix form, where

, , .

Theorem 4.3: A square systemof linear equations has a unique solution if and only if the matrix is invertible. In such case, is a unique solution of the system.

Prove:

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