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Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Veri...

Let `A = [[1,-2,1],[-2,3,1],[1,1,5]]` Verify that `[adj A]^-1 = adj (A^-1)`

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that: |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c...

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  2. If A^-1 = [[3,-1,1],[-15,6,-5],[5,-2,2]] and B = [[1,2,-2],[-1,3,0],[0...

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  3. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that [adj A]^-1 = adj (A^-1...

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  4. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that (A^-1)^-1 = A

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  5. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

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  6. Evaluate |[1,x,y],[1,x+y,y],[1,x,x+y]|

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  7. Using properties of determinants, prove that: |[alpha,alpha^2,beta+gam...

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  8. Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1...

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  9. Solve by matrix method 2/x + 3/y + 10/z = 4 , 4/x - 6/y + 5/z = 1 , ...

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  10. 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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  11. Let A = [[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]], wher...

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  12. Fill in the blanks : If A = [(1,a,3),(2,b,6),(3,c,9)], then det A is...

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  13. Fill in the blanks : If cos 2 theta = 0, then |(0, costheta, sinthet...

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  14. Fill in the blanks : Determinant of a skew symmetric matrix of order...

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

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  16. Fill in the blanks : If A is an invertible square matrix, then (A)^-...

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  17. If A is matrix of order 3xx3, then (A^(2))^(-1)=…….

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  18. Fill in the blanks : The determinant of a diagonal matrix is equal t...

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  19. The sum of the products of elements of any row with the co-factors of ...

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  20. If A is matrix of order 3xx3, then |3A|=……….

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