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Using properties of determinants, prove the following: `abs{:(a+ b+ 2c , a , b),(c, b + c + 2a , b),(c , a , c + a+ 2b):}= 2 ( a+ b + c)^3.`

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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)

OMEGA PUBLICATION-DETERMINANTS-Multiple Choice Questions (MCQs)
  1. Using properties of determinants, prove the following: abs{:(a+ b+ 2c ...

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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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