1.

सिद्ध किजिये कि `|{:(2y,y-z-x,2y),(2z,2z,z-x-y),(x-y-z,2x,2x):}|=(x+y+z)^(3)`

Answer» बायाँ पक्ष `=|{:(2y,y-z-x,2y),(2z,2z,z-x-y),(x-y-z,2x,2x):}|`
`=|{:(2y,y-z-x,2y),(2z,2z,z-x-y),(x+y+z,x+y+z,x+y+z):}|(R_(3)toR_(1)+R_(2)+R_(3)" से")`
`=(x+y+z)|{:(2y,y-z-x,2y),(2z,2z,z-x-y),(1,1,1):}|`
`=(x-y+z)|{:(0,-(x+y+z),2y),(x+y+z,x+y+z,z-x-y),(0,0,1):}|(C_(1)toC_(1)-C_(3) "तथा"C_(2)toC_(2)-C_(3)"से")`
`=(x+y+z)*1*|{:(0,-(x+y+z)),(x+y+z,(x+y+z)):}|`
`=(x+y+z)[0+(x+y+z)^(2)]`
`=(x+y+z)^(3)=` दायाँ पक्ष


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