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Tuesday 25 October 2011

Inverse of Matrix by Gauss-Jordan elimination Aljabar linier

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 In to obtain A-1.

Inverse of 2 x 2 matrices

Example 1: Find the inverse of
Inverse of 2 x 2 matrices
Solution:
Step 1: Adjoin the identity matrix to the right side of A:
Inverse of 2 x 2 matrices
Step 2: Apply row operations to this matrix until the left side is reduced to I. The computations are:
Inverse of 2 x 2 matrices
Step 3: Conclusion: The inverse matrix is:
Inverse of 2 x 2 matrices

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
Not invertible matrix
Solution:
Step 1: Adjoin the identity matrix to the right side of A:
Not invertible matrix
Step 2: Apply row operations
Not invertible matrix
Step 3: Conclusion: This matrix is not invertible.

Inverse of 3 x 3 matrices

Example 1: Find the inverse of
Inverse of 3 x 3 matrices
Solution:
Step 1: Adjoin the identity matrix to the right side of A:
Inverse of 3 x 3 matrices
Step 2: Apply row operations to this matrix until the left side is reduced to I. The computations are:
Inverse of 3 x 3 matrices
thanks for http://www.mathportal.org/linear-algebra/matrices/gauss-jordan.php

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