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

Evaluate `[[1,a,b+c],[1,b,c+a],[1,c,a+b]]`

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Evaluate [[1,a,bc],[1,b,ca],[1,c,ab]]-[[1,a,a^2],[1,b,b^2],[1,c,c^2]]

Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,c^2]]

Find the value of [[1,a,b+a],[1,b,c+a],[1,c,a+b]] .

Fill in the blanks with appropriate answer from the brackes. [[1,a,b+c],[1,b,c+a],[1,c,a+b]] =_______

What is the value of abs[[a,b+c,1],[b,c+a,1],[c,a+b,1]] ?

Prove that [[1,a,a^2 - bc],[1,b,b^2 - ca],[1,c,c^2 - ab]]

Evaluate [[a,a^2-bc,1],[b,b^2-ac,1],[c,c^2-ab,1]]

Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]] =0

Using properties of determinants , prove that |{:(1,a,bc),(1,b,ca),(1,c,ab):}|=(a-b)(b-c)(c-a)

Find the value of |[a-b,b+c,a],[b-a,c+a,b],[c-a,a+b,c]| ?

MODERN PUBLICATION-DETERMINANTS-PROBLEM
  1. For what k, x - ky = 0 kx - y - z = 0 x + y - z = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[...

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  20. Prove that the following. [[a+d,a+d+k,a+d+c],[c,c+b,c],[d,d+k,d+c]]=ab...

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