Definition, Formula, Solved Example Problems, Exercise | Mathematics - Inverse of a matrix | 11th Business Mathematics and Statistics(EMS) : Chapter 1 : Matrices and Determinants
Chapter: 11th Business Mathematics and Statistics(EMS) : Chapter 1 : Matrices and Determinants
Inverse of a matrix
Inverse of a matrix
1. Singular matrix
A Square matrix A is said to be singular,
if A
= 0
2. Non – singular matrix:
A square matrix A is said to be non – singular, if
A Î 0
3. Adjoint of a Matrix
The adjoint of a square matrix A is defined as the transpose of a
cofactor matrix. Adjoint of the matrix A
is denoted by adj A
4. Inverse of a matrix
Let A
be any non-singular matrix of order n.
If there exists a square matrix B of order n
such that AB = BA = I then, B is called the inverse of A and is
denoted by A-1
5. Solution of a system of linear equations
Consider a system of n linear non – homogeneous
equations with n unknowns x1 ,
x2, ......xn as
Example 1.22
The cost of 4 kg onion, 3 kg wheat and 2 kg
rice is `320. The cost of 2kg onion, 4 kg wheat and 6 kg rice is `560. The cost
of 6 kg onion, 2 kg wheat and 3 kg rice is `380. Find the cost of each item per
kg by matrix inversion method.
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