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Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^...

Given `Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)|` Prove that `Delta=(1+pxyz)(x-y)(y-z)(z-x)`.

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BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. Consider the system of equations x-y+z=3,2x+y-z=2,-x-2y+2z=1. Is A inv...

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  2. Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Express thi...

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  3. Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Prove that ...

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  4. Ashok purchased 3 pencils, 2 instrument boxes and 1 pen and paid Rs 41...

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  5. Ashok purchased 3 pencils, 2 instrument boxes and 1 pen and paid Rs 41...

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  6. If A=[(1,2,-3),(2,3,2),(3,-3,-4)] Is A non-singular? Why?

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  7. If A=[(1,2,-3),(2,3,2),(3,-3,-4)] find A^-1.

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  8. If A=[(1,2,-3),(2,3,2),(3,-3,-4)] Solve the system of linear equations...

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  9. 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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  10. Ifabs[[1,-3,2],[4,-1,2],[3,5,2]]=40,thenabs[[1,4,3],[-3,-1,5],[2,2,2]]...

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  11. Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

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  12. Let the value of a determinant is Delta. Then the value of a determi...

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  13. Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],...

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  14. The value of the determinant |(sin10,-cos10),(sin50,cos50)| is a)-1 b)...

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  15. Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2...

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  16. Choose the correct answer from the bracket.The value of the determin...

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  17. Consider abs[[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]]

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  18. Choose the correct answer from the bracket.Consider a sqare matrix o...

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  19. Verify A(adjA)=(adjA)A=abs[A]I for the matrix A=[[5,-2],[3,-2]]that,...

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  20. Choose the correct answer from the bracket. If A=[(cosx,sinx),(-sinx,c...

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