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Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2...

Prove that `|(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)`

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Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

Value of |(1,a,a^2),(1,b,b^2),(1,c,c^2)| is (A) (a-b)(b-c)(c-a) (B) (a^2-b^2)(b^2-c^2)(c^2-a^2) (C) (a-b+c)(b-c+a)(c+a-b) (D) none of these

1,1,1a,b,ca^(2),b^(2),c^(2)]|=(a-b)(b-c)(c-a)

Show that |(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)

([1,1,1a,b,ca^(2),b^(2),c^(2)])=(a-b)(b-c)(c-a)

Prove that |{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=0

Prove that det[[1,a,a^(2)-bc1,b,b^(2)-ca1,c,c^(2)-ab]]=0

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Without expanding the determinant , prove that |{:(a, a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=|{:(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3)):}|

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

MODERN PUBLICATION-DETERMINANTS-NCERT FILE (Exercise 4.2)
  1. Using the property of determinants and without expanding, prove that:...

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  2. Using the property of determinants and without expanding, prove that:...

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  3. Using the property of determinants and without expanding, prove that |...

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  4. Using the property of determinants and without expanding, prove that:...

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  5. Use the properties of determinant and without expanding prove that |...

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  6. By using properties of determinants in |{:(0,a,-b),(-a,0,-c),(b,c,0):}...

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  7. Using properties of determinants, prove that |-a^2a b a c b a-b^2b cc...

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  8. Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

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  9. Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b...

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  10. [[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

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  11. By using properties of determinants. Show that: (i) |x+4 2x2x2xx+4 2x2...

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  12. Prove, using properties of determinants: |y+k y y y y+k y y y y+k|=k^...

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  13. Prove that: |[a-b-c, 2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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  14. Prove that Det[[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]]=2(x+y+z)^3

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  15. By using properties of determinants. Show that:|1xx^2x^2 1xxx^2 1|=(1-...

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  16. Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2...

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  17. Using properties of determinants, prove the following: |a^2a b a c...

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  18. Let A be a square matrix of order 3xx3, then |k A|is equal to(A) k|A|...

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  19. Which of the following is correct ?

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