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If u=a x^2+2b x y+c y^2,\ y^(prime)=a^('...

If `u=a x^2+2b x y+c y^2,\ y^(prime)=a^('2)+2b^(prime)x y+c^(prime)y^2,` then prove that- `|y^2-x y x^2a b c a ' b ' c '|=|a x+b y b x+c y a^(prime)x+b ' y b^(prime)x+c ' y|=-1/y|uu ' a x+b y a^(prime)x+b ' y|`

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ALLEN -DETERMINANTS-All Questions
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  3. If u=a x^2+2b x y+c y^2,\ y^(prime)=a^('2)+2b^(prime)x y+c^(prime)y^2,...

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  4. If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y...

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  5. If x,y and y are not all zero and if ax+by+cz=0,bx+cy+az=0 and cx...

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  7. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  9. If D=|[1, 1, 1], [1, 1+x, 1], [1, 1, 1+y]| for x!=0, y!=0 then D is (1...

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  14. If the trivial solution is the only solution of the system of equation...

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  18. Statement 1: The system of linear equations x+(sinalpha)y+(cosalpha)z=...

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  19. Consider the system of equations x+a y=0,\ y+a z=0\,z+a x=0.\ Then th...

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