2. Qn: 5 a Three types of TV P,Q,R are assembled in a small scale industry and three types of valves A,B, and C are
available. The number of different types of valves used in each tv are given below
Types of TV No. of types of values
A B C
P 1 2 3
Q 3 2 1
R 2 1 3
If the total number of values of the types A,B and f used by the industry are 42, 34 and 56 respectively, find out
the number of each type of tv assembled
• Let x,y,z be the number of TV of Type P Q and R
• Then,
• x+3y+2z = 42
• 2x+2y+z = 34
• 3x+y+3z=56
• Here,
• A =
1 3 2
2 2 1
3 1 3
X =
𝑥
𝑦
𝑧
and B =
42
34
56
• 𝐴 =
1 3 2
2 2 1
3 1 3
• = 1(6-1) -3(6-3)+2(2-6)
• = 5-9-8
• -12
• Now , AX = B
• So, X = A-1B