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Factorize the following. [[x+a,b,c],[b,x...

Factorize the following. `[[x+a,b,c],[b,x+c,a],[c,a,x+b]]`

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Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]] =(b-c)(c-a)(a-b)(bc+ca+ab)

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

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

Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =2(b+c)(c+a)(a+b)

Prove that the following. [[a,a^2,a^3],[b,b^2,b^3],[c,c^2,c^3]] = abc(a-b)(b-c)(c-a)

Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]] =(b-c)(c-a)(a-b)

Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] = a^3+b^3+c^3-3abc

Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

ARIHANT PUBLICATION-DETERMINANTS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 5(A))
  1. Solve the following : [[7,6,x],[2,x,2],[x,3,7]]=0

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  2. Solve the following : [[0,x-a,x-b],[x+a,0,x-c],[x+b,x+c,0]]=0

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  3. Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

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

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  5. Solve the following : [[1,4,20],[1,-2,5],[1,2x,5x^2]]=0

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

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

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  8. Solve the following : [[x,1,3],[1,x,1],[3,6,3]]=0

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  9. Evaluate the following : [[2,3,4],[1,-1,3],[4,1,10]]

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  10. Evaluate the following :[[x,1,2],[y,3,1],[z,2,2]]

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  11. Evaluate the following :[[x,1,-1],[2,y,1],[3,-1,z]]

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  12. Evaluate the following :[[a,h,g],[h,b,f],[g,f,c]]

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  13. Evaluate the following : [[8,-1,-8],[-2,-2,-2],[3,-5,-3]]

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  14. Evaluate the following : [[sin^2theta,cos^2theta,1],[cos^2theta,sin^2t...

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  15. Evaluate the following : [[-1,3,2],[1,3,2],[1,-3,-1]]

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  16. Evaluate the following : [[11,23,31],[12,19,14],[6,9,7]]

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  17. Evaluate the following : [[37,-3,11],[16,2,3],[5,3,-2]]

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  18. Evaluate the following : [[2,-3,4],[-4,2,-3],[11,-15,20]]

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  19. Show that x=1 is a solution of [[x+1,3,5],[2,x+2,5],[2,3,x+4]]=0

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  20. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

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