Page 167 - Artificial Intellegence_v2.0_Class_11
P. 167
Take the second row of matrix A and first column of matrix B. Multiple the corresponding elements and then add them
as shown. Repeat this step for all columns of B.
Step 4: 51 26 0
A = B=
23 13 4
11 33 4
×
⇒ 2 2 31 ⇒ 7 ⇒
+
×
7 ? ?
Step 5: 51 26 0
A = B =
23 13 4
11 33 4
×
⇒ 2 6 3 3 ⇒ 21⇒
×
+
7 21 ?
Step 6: 51 26 0
A = B =
23 13 4
11 33 4
+
×
⇒ 2 034⇒ 12 ⇒
×
7 21 12
Finally AB = 11 33 4
7 21 12 23
×
Reboot
1. If a matrix has 6 elements, what are the possible orders it can have?
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2i
2. Construct a 3 x 2 matrix where each element is given by a = .
ij
j
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Determinants
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. This function
can be a real number or a complex number, but it is unique. The determinant of a matrix A is denoted by det(A), det
A, or |A|.
1. Determinant of 1x1 matrix: The determinant of a matrix A= [a ] is the element a . For example:
ij
ij
A 11 A3
=
=
3
×
2. Determinant of 2 x 2 matrix: If A is a 2 x 2 matrix then the determinant of A is defined as a a – a a .
21 12
11 22
a a
−
A = 11 12 A = ( a × a ) ( a × a )
12
21
11
a
22
21 a 22
1 3
−− × )
A = A = 1( × 4 ) ( 23 =10
−2 4
Maths for AI 165

