Page 146 - Touhpad Ai

B. Long answer type questions.
 9 1 − 0  1 2 − 1
1. If   =A +   then find the matrix A.
−  2 1 3   0 4 6 

Ans. Given matrix equation can be rewritten as:
 9 1 − 0 1 2 − 1
A =   
−
−  2 1 3  0 4 6 
Subtracting the individual elements
−
 9 1 −− 0 1 +
1 2
A =  
−
2 0
 −− 1 4 3 6  −
 8 − 3 1
=  
 − 2 − 3 − 3 
 24  1 3
2. If A =   and B =   then find A – B.
 62  −  4 5 
 24  1 3
Ans. Given, A =   and B =  
 62  −  4 5 
 24 1 3
−
∴ A B   
−=
 62  − 4 5 
2 1 4 3 −  −
=  
 6 ( 4) 2 5  − − −
 1 1
=  
 10 −  3
3. Find the mean, median and mode of the following data.
Class 0-10 10-20 20-30 30-40 40-50 Total
Frequency 16 8 35 36 5 100

Ans. Class m=(1 +1 )/2 F fm cf
1 2
0-10 5 16 80 16
10-20 15 8 120 24
20-30 25 35 875 59
30-40 35 36 1260 95
40-50 45 5 225 100
Total 125 100 2560

Mean = 2560 = 25.6
100
N 100 = 50th item which lies in class 20-30 (as per cf)
=
2 2
−
Median = 20 + 50 24 x 10
35
= 20 + 7.4 = 27.4
Modal class = 20 – 30 (as per grouping Analysis)
−
35 8
Mode = 20 + x 10
−−
2(35) 8 36
= 20 + 10.38 = 30.38

144 Touchpad Artificial Intelligence - XI