Page 169 - Artificial Intellegence_v2.0_Class_11
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−
−
= 1 (0 40) − 2(0 35) + 3(32 0)
−
+
= − 40 70 96
+
=
A 126
Task
Calculate the determinant of the following matrices:
13 2
1. A = 60 0
75 4
2 4
2. A =
38
Inverse of a Matrix
For matrices, division is undefined. There is a related concept, called “inversion”. Matrix inversion is a process of
finding another matrix that when multiplied with the original matrix, gives an identity matrix.
1 1
6 6× = 1
Reciprocal 6 6
–1
A A –1 A × A = I (Identity Matrix)
Inverse
Calculating Inverse of a Matrix
Following are the steps in order to calculate the inverse of a matrix:
• Inverse of 2x2 Matrix: Consider matrix A given by:
ab
A =
cd
-1
Then the inverse of the matrix A, denoted by A is given by:
1 d − b This matrix is also
−
A = called adjoint.
1
A − c a
determinant
Rules:
1. To calculate the adjoint of a matrix – In matrix A, SWAP (interchange) the positions of elements a and d. Also,
put a negative (minus) sign in front of elements b and c.
2. Divide all elements by the determinant.
For example:
65
Find the inverse of A =
21
65
×− ×= − 4
A = = 61 25
21
Maths for AI 167

