The elementary row transformation of matrix A is equivalent to the left multiplication elementary matrix, and the elementary column transformation of matrix A is equivalent to the right multiplication elementary matrix.

Elementary matrix:

Eij: swap I and j rows (columns)

Ei(k): multiply the i-th row (column) by k.

Eij(k): Multiply the k in line I (column) by line J (column).

Matrix operation formula: (ab)-1= b-1a-1.

(Eij)- 1 = Eij

(Ei(k))- 1 = E i ( 1/k)

(Eij(k))- 1 = Eij(-k)

The answer (the question is not clear) is taken literally.

Matrix A is transformed into EijA by ① transformation.

Then it is transformed into Ej(c) EijA by ② (at this time, I line is considered as I line mentioned in the previous step and has been changed to J line).

Then it is transformed into Eij( 1) Ej(c) EijA through ③ transformation.

[Eij( 1)Ej(c)EijA]- 1 = A- 1 eijej(-c)Eij( 1)

That is, A- 1 is converted as follows:

Interchange the I column and J column of A- 1

Multiply the j column by -c times.

Then add column I to column J.

Newman Hero 2065438+February 9, 2005 09:04:44

I hope it will help you and I hope it will be adopted.