SUBMITTED BY:

Syed Ahmed Zaki

ID No: 131-15-2169Section: A

Dept. of Computer Science and Engineering

1st year,2nd Semester

Summer 2013

Submission Date : 19 August 2013

SUBMITTED TO:

Mohammad Salek ParvezAssistant Professor

Department of Natural Science

Faculty of Science and Information Technology

Daffodil International University

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 ‘𝑀−1’ and is such a matrix that 𝑀𝑀−1=

𝑀−1𝑀=𝐼𝑛

Matrix ‘M’ is said to be invertible if 𝑀−1 𝑒𝑥𝑖𝑠𝑡𝑠. 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

EXAMPLE

Example:

M= 4 33 2

and It’s inverse is 𝑀−1 =−2 33 −4

since

𝑀𝑀−1=4 33 2

−2 33 −4

= 1 00 1

𝑀−1𝑀=−2 33 −4

4 33 2

= 1 00 1

Therefore, 4 33 2

and −2 33 −4

are inverses of each other

There are usually two methods to find the

inverse of a matrix. These are:

(a) Crammer’s Method

(b) Gauss Method

METHOD

CRAMMER’S METHOD

Equation:

𝑀−1 = 1

𝑀(adj M)

Flowchart :

•Matrix M• Cofactor M[Cof (M) ]

• Adjoint M[adj (M) ]

• Inverse Matrix:𝑀−1

EXAMPLE

GAUSS METHOD FOR INVERSION

SHORTCUT METHOD

THE END