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Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x...

Prove that `a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0` represents a straight line parallel to the y-axis.

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  7. Show that the determinant |a^2+b^2+c^2 bc+ca+ab bc+ca+ab bc+ca+ab a^2+...

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  9. If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, th...

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  17. If |[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7],[x,7, 2],[ 7, 2,x]|=|[4, 5,x]...

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  18. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

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  19. If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...

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