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By using properties of determinants. Sho...

By using properties of determinants. Show that:`|[x,x^2,y z],[ y, y^2,z x],[ z, z^2,x y]|=(x-y)(y-z)(z-x)(x y+y z+z x)`

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Given LHS`=|[x,x^2,y z],[ y, y^2,z x],[ z, z^2,x y]|`
Applying `R_1->R_1-R_2`
`=|[x-y,x^2-y^2,yz-xz],[ y, y^2,z x],[ z, z^2,x y]|`
`=|[x-y,(x-y)(x+y),-z(x-y)],[ y, y^2,z x],[ z, z^2,x y]|`
...
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NCERT ENGLISH-DETERMINANTS-All Questions
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  2. Using the property of determinants and without expanding, prove that:...

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  3. By using properties of determinants. Show that:|[x,x^2,y z],[ y, y^2,z...

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  4. By using properties of determinants. Show that: (i) |[1,a, a^2],[ 1,...

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  5. If a, b, c are positive and unequal, show that value of the determina...

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  7. Show that Delta=|((y+z)^2,xy,zx),(xy,(x+z)^2,yz),(xz,yz,(x+y)^2)|=2x y...

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  12. By using properties of determinants. Show that:|[1,x,x^2],[x^2, 1,x],[...

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  13. By using properties of determinants. Show that:|[1+a^2-b^2, 2a b,-2b],...

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  16. Which of the following is correct (A)   Determinant is a square matrix...

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  19. Examine the consistency of the system of equations x + 3 y = 5" "2x + ...

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  20. Examine the consistency of the system of equations 2x - y = 5" "x + y ...

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