**Inverse of Matrix by Gauss-Jordan elimination Aljabar linier**.

Mata kuliah saya diantaranya aljabar Linier. waduh susah dah. dengan latar belakang sms.. akibat googling.. saya mendapat kan jawaban.. tra tar.

To find the inverse of matrix A, using Gauss-Jordan elimination, we must find a sequence of elementary row operations that reduces A to the identity and than perform the same operations on I

_{n}to obtain A^{-1}.### Inverse of 2 x 2 matrices

Example 1: Find the inverse of

Solution:

**Step 1:**Adjoin the identity matrix to the right side of A:

**Step 2:**Apply row operations to this matrix until the left side is reduced to I. The computations are:

**Step 3:**Conclusion: The inverse matrix is:

### Not invertible matrix

**If A is not invertible**, then, a zero row will show up on the left side.

Example 2: Find the inverse of

Solution:

**Step 1:**Adjoin the identity matrix to the right side of A:

**Step 2:**Apply row operations

**Step 3:**Conclusion: This matrix is not invertible.

### Inverse of 3 x 3 matrices

Example 1: Find the inverse of

Solution:

**Step 1:**Adjoin the identity matrix to the right side of A:

**Step 2:**Apply row operations to this matrix until the left side is reduced to I. The computations are:

**thanks for http://www.mathportal.org/linear-algebra/matrices/gauss-jordan.php**

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