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By using properties of determinants, sh...

By using properties of determinants, show that : `|[1,1,1],[a,b,c],[a^3,b^3,c^3]| = (a-b)(b-c)(c-a)(a+b+c)`

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Using the properties of determinants show that : |[[1,1,1],[a^2,b^2,c^2],[a^3,b^3,c^3]]|=(a-b)(b-c)(c-a)(ab+bc+ca) .

By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2],[1,c,c^2]| = (a-b)(b-c)(c-a)

Using the properties of determinants show that : |[[a^2, b^2, c^2],[bc,ca,ab],[a,b,c]]|=(a-b)(b-c)(c-a)(ab+bc+ca)

By using properties of determinants, Show that : {:|(0,a,-b),(-a,0,-c),(b,c,0)|=0

Prove that |[[a,b,c],[a^2,b^2,c^2],[a^3,b^3,c^3]]|= abc (a-b)(b-c)(c-a)

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1,b^2+ac,b^3],[1,c^2+ab,c^3]]|=(a-b)(b-c)(c-a)(a^2+b^2+c^2)

Using the properties of determinants, prove that : |[[x+a,b,c],[a,x+b,c],[a,b,x+c]]| = x^2(x+a+b+c)

Using properties of determinants, prove that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]| = 3(a+b+c)(ab+bc+ca)

OMEGA PUBLICATION-DETERMINANTS-Multiple Choice Questions (MCQs)
  1. By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^...

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  2. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x is equal to:

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  3. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  4. If A is an invertible matrix of order n, then |adj A|=

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  5. If area of triangle is 35 sq. units with vertices (2, - 6), (5, 4) and...

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  6. Delta=|(a(11),a(12),a(13)),(a(21),a(22),a(23)),(a(31),a(32),a(33))| an...

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  7. Let A be a non-singular matrix of order 3 xx 3. Then I adj. A I is equ...

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  8. Select the Correct Option If A is an invertible matrix of order 2, the...

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  9. If a, b, c are in A.P., then the determinant abs{:(x+2, x+3, x+2a),(x+...

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  10. If x, y, z are non-zero real numbers, then the inverse of matrix A = [...

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  11. Let A = [{:(1, sin theta , 1),(-sin theta, 1 , sin theta),(-1 , - sin ...

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  12. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x is equal to:

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  13. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  14. If A is an invertible matrix of order n, then |adj A|=

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  15. If area of triangle is 35 sq. units with vertices (2, - 6), (5, 4) and...

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  16. Delta=|(a(11),a(12),a(13)),(a(21),a(22),a(23)),(a(31),a(32),a(33))| an...

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  17. Let A be a non-singular square matrix of order 3×3. Then abs(adjA) is

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  18. lf A is an invertible matrix of order 2, then |A^(-1) | is equal to

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  19. If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a],[x+3,x+4,...

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  20. If x. y, z are non- real number", then the inverse of matrix A = [[x,0...

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  21. Let A = [{:(1, sin theta , 1),(-sin theta, 1 , sin theta),(-1 , - sin ...

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