Multiplication of matrices.
Matrix representation of a linear system:
Indentity matrix: .
| Inverse matrix:
Solving a sytem of n linear equations of n variables:
Theorem. If E is an elementary matrix then the matrix is obtained from matrix A by the row operation (1)-(3) corrsponding to E.
|Multiplication of the first row by -5||Interchanging of the first and third rows||Addition 7 times the first row to the third row|
A method for inverting matrices.
Adjoin the identity matrix I to the right side of A producing .
Apply row operations (1)-(3) to this matrix until the left half is reduced to I. The right half will be converted into the inverse matrix: .
Multiply the following matrices.
Find the following inverses.
Find the following inverses and their representation as the product of elementary matrices.
Find the inverses.
5. Solve matrix equation