Echelon Form Of Matrix

Echelon Form of Matrix-1:

An m n matrix B is said to be row (column) equivalent to an m n A if B can be obtained by applying a finite sequence of elementery row (column) operations to A.

Example-3: Let

If we add 2 times rows 3 of A its second row, we obtain

So B is the row equivalent to A.

Interchanging rows 2 and 3 of B we get;

'

Hence C is row equivalence to B.

Find the Inverse of matrix by Row Operations:

If A is non singular matrix then by applying row operation we can transform matrix [ A|I ] to matrix [ I|B ]. In this case B is the inverse of A. We summarize the process by diagram below:

Example-4: Find the inverse of

By applying the above rule we get;