1.

Prove that `|{:(1,x+alpha,y+z-alpha),(1,t+beta,+x-beta),(1,z+gamma,x+y-gamma):}|=0`

Answer» `L.H.S.=|{:(1,x+alpha,y+z-alpha),(1,t+beta,+x-beta),(1,z+gamma,x+y-gamma):}|`
`=|{:(1,x+alpha,y+z-alpha),(1,t+beta,+x-beta),(1,z+gamma,x+y-gamma):}|(C_(3)toC_(3)+C_(2))`
`=(x+y+z)|{:(1,x+alpha,1),(1,t+beta,1),(1,z+gamma,1):}|`
`=0 " "(therefore C_(1)" and "C_(3)" are same")`
`=R.H.S." "Hence Proved`.


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