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

`x+y+z=6 ldots (i)`

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3 z+y=11 ldots (ii) `

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x+z=2 y ldots (iii) `

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

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R_{2}: R_{2} rightarrow R_{3}`

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

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R_{2} ; R_{2}-R_{1}`

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

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