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Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],...

Show that: `|[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3`

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

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

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

Using properties of determinants, show that: |[[(b+c)^2, a^2, a^2],[b^2, (c+a)^2, b^2],[c^2,c^2,(a+b)^2]]|= 2abc (a+b+c)^3 .

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)

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

Prove that: |[a+b, b+c, c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]|=2|[a,b,c],[b,c,a],[c,a,b]|

OMEGA PUBLICATION-DETERMINANTS-Multiple Choice Questions (MCQs)
  1. Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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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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