Question

the sum of 3 numbers is 6. if we multiply third number by 3 and add it to the second number we get 11.by adding first and third number we get a number which is double the second number use this information and find a system of linear equation.find the 3 number using matrices

Answer 1

the numbers are 1,2,3... 
x+y+z=6
3z+y=11
x+z=2y
solving all these we get 1,2&3

Answer 2

I don't think that matrices are used . The statements can be represented by equations as follows :-
Statement 1) → a + b + c = 6
Statement 2) → 3c + b = 11
Statement 3) → a + c = 2b
 Substituting a + c in equation 1
⇒2b + b = 6
⇒3b = 2
⇒ b = 2

Substituting value of b in equation 2
⇒3c + 2 = 11
⇒3c = 9
⇒c = 3

Substituting c in equation 3
⇒ a + 3 = 4
⇒a = 1

∴ a = 1 ; b = 2 ; c = 3