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IF |{:(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2...

IF `|{:(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3):}|=0` , then show that abc=1

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SRISIRI PUBLICATION-MATRICES-SHORT ANSWER TYPE QUESTIONS
  1. Show that |(b+c,c+a,a+b),(a+b,b+c,c+a)(a,b,c)|=a^(3)+b^(3)+c^(3)-3abc.

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  2. Prove that |{:(y+z,x,x),(y,z+x,y),(z,z,x+y):}|=4xyz

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  3. IF |{:(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3):}|=0 , then show that ...

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  4. Without expanding the determinant , prove that |{:(a,a^2,bc),(b,b^2,ca...

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  5. Without expanding the determinant , prove that |{:(ax,by,cz),(x^2,y^2,...

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  6. Without expanding the determinant, prove that |{:(1,bc,b+c),(1,ca,c+a)...

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  7. Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

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  8. Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0

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  9. Let A and B be invertible matrices then prove that (AB)^-1=B^-1A^-1.

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  10. Find the adjoint and the inverse of the matrix A=[{:(1,3,3),(1,4,3),(1...

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  11. Show that the matrix A=[{:(1,2,1),(3,2,3),(1,1,2):}] is non-singular a...

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  12. IF abc ne 0, find the inverse of [{:(a,0,0),(0,b,0),(0,0,c):}]

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  13. IF A=[{:(-1,-2,-2),(2,1,-2),(2,-2,1):}] then show that adj A=3A^T. Als...

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  14. IF A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] then show that A^-1=A^3.

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  15. IF 3A=[{:(1,2,2),(2,1,-2),(-2,2,-1):}] then show that A^-1=A'.

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  16. Find the rank of A=[{:(0,1,2),(1,2,3),(3,2,1):}] using elementary tran...

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  17. Find the rank of A=[{:(1,2,0,-1),(3,4,1,2),(-2,3,2,5):}] using element...

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  18. If A is a non-singular matrix then prove that A^(-1) = (adjA)/(|A|).

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  19. Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-...

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  20. Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(a...

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