The sum of three numbers is 6. If we multiply the third number 2 and add the first number to the result, we get 7. Be adding second and third numbers to three times the first number we get 12. Use determinants to find the numbers.

Explanation

Let the first , second & third number be x,y,z respectively
Given,

`x+y+z=6 `

` y+3z=11 `

`x+z=2y `or `x-2y+z=0`

We can write them in matrix from AX=B....(i)

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

Determinant of matrix A,

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