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By using the properties of determinants,...

By using the properties of determinants,prove that
`|[1+a^2-b^2,2ab ,-2b],[2ab,1-a^2+b^2,2a],[2b ,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3`

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Prove |[1+a^2-b^2, 2 a b, -2 b],[ 2 a b, 1-a^2+b^2, 2 a],[ 2 b, -2 a, 1-a^2-b^2]|=(1+a^2+b^2)^3

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By using the properties of determinants,prove that |[a^2+1,ab ,ac],[ab,b^2+1,bc],[ca ,cb,c^2+1]|=1+a^2+b^2+c^2

By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

Using properties of determinants prove the following. abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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

Without expanding the determinant, Prove that |[a,a^2, bc],[b,b^2,ca],[c,c^2,ab]|= |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+...

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

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

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

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

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  6. Which of the following is correct?

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

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

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

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

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

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

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

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

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

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

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

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

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  20. If A =[[3,1],[-1,2]],show that A^2-5A + 7I=0 Hence, find A^(-1)

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