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# Presentation on inverse matrix

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Presentation on inverse matrix

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### Presentation on inverse matrix

1. 1. SUBMITTED BY: Syed Ahmed Zaki ID No: 131-15-2169 Section: A Dept. of Computer Science and Engineering 1st year,2nd Semester Summer 2013 Submission Date : 19 August 2013
2. 2. SUBMITTED TO: Mohammad Salek Parvez Assistant Professor Department of Natural Science Faculty of Science and Information Technology Daffodil International University
3. 3. INVERSE MATRIX As usual the notion of inverse matrix has been developed in the context of matrix multiplication.Every nonzero number possesses an inverse with respect to the operation ‘number multiplication’ Definition: Let ‘M’ be any square matrix.An inverse matrix of ‘M’ is denoted by ‘푀−1’ and is such a matrix that 푀푀−1= 푀−1푀=퐼푛 Matrix ‘M’ is said to be invertible if 푀−1 푒푥푖푠푡푠. Non-square matrices do not have inverses. Note: Not all square matrices have inverses. A square matrix which has an inverse is called invertible or nonsingular, and a square matrix without an inverse is called noninvertible or
4. 4. EXAMPLE Example: M= 4 3 3 2 and It’s inverse is 푀−1 = −2 3 3 −4 since 푀푀−1= 4 3 3 2 −2 3 3 −4 = 1 0 0 1 푀−1푀= −2 3 3 −4 4 3 3 2 = 1 0 0 1 Therefore, 4 3 3 2 and −2 3 3 −4 are inverses of each other
5. 5. METHOD There are usually two methods to find the inverse of a matrix. These are: (a) Crammer’s Method (b) Gauss Method
6. 6. CRAMMER’S METHOD Equation: 푀−1 = 1 푀 (adj M) Flowchart : •Matrix M • Cofactor M[Cof (M) ] • Adjoint M[adj (M) ] • Inverse Matrix:푀−1
7. 7. EXAMPLE
8. 8. GAUSS METHOD FOR INVERSION
9. 9. SHORTCUT METHOD
10. 10. THE END