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|[1,x,x^(2)],[x^(2),1,x],[x,x^(2),1]|...

|[1,x,x^(2)],[x^(2),1,x],[x,x^(2),1]|

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Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

Using properties of determinants prove the following. abs[[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

By using properties of determinants , show that : {:[( 1,x,x^(2) ),( x^(2) ,1,x) ,( x,x^(2), 1) ]:} =( 1-x^(3)) ^(2)

By using properties of determinants , show that : {:[( 1,x,x^(2) ),( x^(2) ,1,x) ,( x,x^(2), 1) ]:} =( 1-x^(3)) ^(2)

A(x)=|(1,2,3),(x+1,2x+1,3x+1),(x^(2)+1,2x^(2)+1,3x^(2)+1)|impliesint_(0)^(1)A(x)dx=

A(x)=|(1,2,3),(x+1,2x+1,3x+1),(x^(2)+1,2x^(2)+1,3x^(2)+1)|impliesint_(0)^(1)A(x)dx=

A(x)=|{:(1,2,3),(x+1,2x+1,3x+1),(x^(2)+1,2x^(2)+1,3x^(2)+1):}|rArrint_(0)^(1)A(x)dx=