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Prove that abs[[a-b-c,2a,2a],[2b,b-c-a...

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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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[[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]] =2abc(a+b+c)^3

If Delta=[(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)] Perform R_1rarrR_1+R_2+R_3 on Delta

prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

If Delta=[(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)] Perform R_1rarrR_1+R_2+R_3 on Delta . Take (a+b+c) common from R_1 & rewrite Delta .

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

Show that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)

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

A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. By using properties of determinants, prove that |[x+4,2x,2x],[2x,x+4,...

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

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

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

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

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

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

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  9. Which of the following is correct?

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

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

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

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

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

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

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

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

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

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

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

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