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If [[a(1),b(1)],[c(1),d(1)]] = k[[a(1),c...

If `[[a_(1),b_(1)],[c_(1),d_(1)]] = k[[a_(1),c_(1)],[b_(1),d_(1)]]` then what is the value of k ?

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MODERN PUBLICATION-DETERMINANTS-PROBLEM
  1. If [[2,4],[k,6]] = 0, what is the value of k ?

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  2. If [[a(1),b(1)],[c(1),d(1)]] = k[[a(1),c(1)],[b(1),d(1)]] then what is...

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  3. If A = ((1,0,2),(5,1,x),(1,1,1)) is a singular matrix the, what is the...

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  4. For what k, x - ky = 0 kx - y - z = 0 x + y - z = 0

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  5. Evaluate [[-6,0,0],[3,-5,7],[2,8,11]

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  6. Evaluate [[1,a,b+c],[1,b,c+a],[1,c,a+b]]

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  7. Find x if [[a,b,c],[b,a,c],[x,b,c]] =0

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  8. Solve the following : [[1+x,1,1],[1,1+x,1],[1,1,1+x]]=0

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  9. Solve the following : [[2,2,x],[-1,x,4],[1,1,1]]=0

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  10. Is ((1,2),(3,4)) invertible, justify ?

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  11. Evaluate the following determinants: [[1^2,2^2,3^2],[2^2,3^2,4^2],[3...

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  12. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

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  13. If Aand B are square matrices of order 3, such that |A| = -1,|B| = 3 t...

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  14. For what k x+2y-3z = 2 (k+3)z = 3 (2k+1) +z = 2 is inconsisten...

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  15. The sum of two non integral roots of [[x,2,5],[3,x,3],[5,4,x]] = 0 is ...

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  16. What is the inverse of A = ((cos alpha,sin alpha),(sin alpha,-cos alph...

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  17. The value of [[1,2,3],[3,5,2],[8,14,20]] is .

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  18. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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  19. Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4ab

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  20. Solve : [[7,6,x],[2,x,2],[x,3,7]] = 0

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