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The Sum of Three Numbers is 6. If We Multiply the Third Number by 3 and Add It to the Second Number We Get 11. by Adding First and Third Numbers We Get a Number, Which is Double than the Second Numbe - HSC Commerce (Marketing and Salesmanship) 12th Board Exam - Mathematics and Statistics

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Question

The sum of three numbers is 6. If we multiply the third number by 3 and add it to the second number we
get 11. By adding first and third numbers we get a number, which is double than the second number. Use
this information and find a system of linear equations. Find these three numbers using matrices.

Solution

Let the three numbers are x, y and z according to
condition
x+y+z=6                    ..........(1)

3z+y=11                     .............(2) 

x+z=2y                       ............(3) 

`[[1,1,1],[0,1,3],[1,-2,1]][[x,],[y,],[z,]]=[[6,],[11,],[0,]]` 

`R_2:R_2↔R_3` 

`[[1,1|,0],[1,-2,1],[1,1,3]][[x,],[y,],[z,]]=[[6,],[0,],[11,]]` 

`R_2:R_2-R_1` 

`[[1,0,0,],[1,-3,1,],[1,0,3,]][[x,],[y,],[z,]]=[[6,],[-6,],[11,]]` 

`R_3:3R_3+R_2` 

`[[1,0,0],[1,1,0],[1,0,9]][[x,],[y,],[z,]][[6,],[-6,],[27,]]` 

`R_3:R_3/9,R_2:R_2/-3` 

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

`R_1:R_1-(R_2+R_3)`

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

`I[[x,],[y,],[z,]]=[[1,],[-2,],[3,]]`

`[[x,],[y,],[z,]]=[[1,],[-2,],[3,]]` 

x = 1, y = 2 and z = 3

  Is there an error in this question or solution?

APPEARS IN

 2017-2018 (March) (with solutions)
Question 2.2.1 | 4.00 marks

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Solution The Sum of Three Numbers is 6. If We Multiply the Third Number by 3 and Add It to the Second Number We Get 11. by Adding First and Third Numbers We Get a Number, Which is Double than the Second Numbe Concept: Inverse of Matrix.
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