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Using properties of determinants prove t...

Using properties of determinants prove the
following.
`abs[[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2`

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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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  2. By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+...

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  3. Using properties of determinants prove the following. abs[[1,x,x^2...

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  4. By using the properties of determinants,prove that |[1+a^2-b^2,2ab ,-...

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  5. By using the properties of determinants,prove that |[a^2+1,ab ,ac],[a...

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  6. Let A be a square matrix of order 2x2 thenabs[KA] is equal to

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  7. Which of the following is correct?

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  8. Consider a triangle whose vertices are (3,8),(-4,2) and (5,1) Find are...

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  9. Find the equation of the line joining A(1,3) and B(0,0) using determin...

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  10. Find the adjoint of A= [(1,2),(3,4)]

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  11. Find the adjoint of B=[[1,-1,2],[2,3,5],[-2,0,1]]

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  12. Verify A (adj A)=(adj A)A=|A|I in the following matrices. [[2,3],[-4,-...

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  13. Verify A (adj A)=(adj A)A=|A|I in the following matrices. [[2,3],[-4,-...

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  14. Find the inverse of the following matrics. [[2,-2],[4,3]]

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  15. Find the inverse of the following matrics. [[-1,5],[-3,2]]

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  16. Find the inverse of the following A=[[1,2,3],[0,2,4],[0,0,5]]

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  17. Find the inverse of the following A=[[1,0,0],[3,3,0],[5,2,-1]]

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  18. Find the inverse of the following A=[[2,1,3],[4,-1,0],[-7,2,1]]

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  19. Find the inverse of the following A=[[1,-1,2],[0,2,-3],[3,-2,4]]

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  20. Let A =[[3,7],[2,5]] and B=[[6,8],[7,9]]Verify that (AB)^(-1)=B^(-1)A^...

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