Page 170 - Artificial Intellegence_v2.0_Class_11
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1 1 − 5 (Swapping the positions of a and d
A − 1 =
− 4 − 2 6 giving minus sign to b and c)
1 5 −
= 4 4
1 − 3
2 2
Note, If the determinant of a matrix is zero, then the inverse of that matrix does not exist.
a) Inverse of 3x3 Matrix: Let’s understand this using an example.
2 − 10
Given a matrix A = 1 02 Calculate A -1
1 13
We know that the formula of inverse is:
1
−1
A = ( AdjA )
A ∴ A = − 3
Let’s calculateA first. 0 2 12 10 Let's calculateAdjoint(A)
(
2 −1 0 ⇒ 2 13 − − 1) 13 +0 11 2 − 10
A = 1 0 2 Expanding along rrow1 ⇒20 2) + 3 2) + 0 A = 1 02
(
(
−
−
1 1 3 ⇒− +⇒ − 3 1 13
41
Step 1: Covering the first row and first column.
2 − 1 0
02
0
2
1 0 2 ⇒ 13 ⇒ −⇒ − 2
1 1 3
Step 2: Covering the first row and second column.
2 − 1 0
12
32
1 0 2 ⇒ 13 ⇒ −⇒ 1
1 1 3
Step 3: Cover the first row and third column.
2 − 1 0
10
10
1 0 2 ⇒ 11 ⇒ −⇒ 1
1 1 3
Step 4: Cover the second row and first column.
2 − 1 0
− 10
30
1 0 2 ⇒ 1 3 ⇒− −⇒ − 3
1 1 3
Step 5: Cover the second row and second column.
2 − 1 0
20
60
1 0 2 ⇒ 13 ⇒ −⇒ 6
1 1 3
168 Touchpad Artificial Intelligence (Ver. 2.0)-XI

