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Using Coafactors of elements of third co...

Using Coafactors of elements of third column evaluate `Delta =|{:(1,x,yz),(1,y,zx),(1,z,xy):}|`

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Using coafactors of the elements of third row, evaluate Delta=|{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

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Show that Delta =Delta_1 where Delta=|{:(Ax,x^2,1),(By,y^2,1),(Cz,z^2,1):}|,Delta_1=|{:(A,B,C),(x,y,z),(zy,zx,xy):}|

If x,y and z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}|=0 then show that 1+xyz=0