Advertisement Remove all ads

The sum of three numbers is 9. If we multiply third number by 3 and add to the second number, we get 16. By adding the first and the third number and then subtracting twice the second number from this sum, we get 6. - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

The sum of three numbers is 9. If we multiply third number by 3 and add to the second number, we get 16. By adding the first and the third number and then subtracting twice the second number from this sum, we get 6. Use this information and find the system of linear equations. Hence, find the three numbers using matrices.

Advertisement Remove all ads

Solution

 

Let the three numbers be x, y, z
From the first condition
x + y + z = 9
From the second condition
y + 3z = 16
From the third condition
x – 2y + 2 = 6

x + y + z = 9
y + 3z = 16
x – 2y + z = 6

`[[1,1,1],[0,1,3],[1,-2,1]][[x],[y],[z]]=[[9],[16],[6]]`

`R_3-R_1`

`[[1,1,1],[0,1,3],[0,-3,0]][[x],[y],[z]]=[[9],[16],[-3]]`

`x+ y + z = 9`

`y = 3z = 16 `

`-3y=-3 =>y=1`

`1+3z=16`

`z=5`

`x+1+5=9`

`x=3`

`therefore x=3, y=1, z=5`

 
Concept: Elementary Transformations
  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×