Using determinants, show that the following system of equations is inconsistent: `2x-y+z=4,\ \ \ x+3y+2z=12 ,\ \ \ 3x+2y+3z=10`

Explanation

`[[2 , -1 , 1],[1 , 3 , 2 ],[3 , 2, 3]] [[x],[y],[z]]=[[y],[12],[10]]`



`R_{2}->2 R_{2}-R_{1}`


`R_{3} ->2 R_{3}-3 R_{1}`



`[[2 , -1 , 1] ,[0, 7, 3] ,[0 , 7, 3]][[x],[y],[z]]=[[4],[20],[8] ]`


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