presentation on inverse matrix
TRANSCRIPT
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