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Prove that |{:(x,x+y,x+y+z),(2x,3x+2y,4x...

Prove that `|{:(x,x+y,x+y+z),(2x,3x+2y,4x+3y+2z),(3x,6x+3y,10x+6y+3z):}|=x^3`

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`"Given,"Delta=|{:(x,x+y,x+y+z),(2x,3x+2y,4x+3y+2z),(3x,6x+3y,10x+6y+3z):}|R_2toR_2-2R_1,R_3toR_3-3R_1`
`Delta=|{:(x,x+y,x+y+z),(0,x,2x+y),(0,3x,7x+3y):}|R_3toR_3-3R_2`
`Delta=|{:(x,x+y,x+y+z),(0,x,2x+y),(0,0,x):}|`
Expanding along `C_1`, we obtain
`Delta=x|{:(x,2x+y),(0,x):}|+0+0`
`=x(x^2-0)=x^3`
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