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Show that without expanding at any stage...

Show that without expanding at any stage
`|{:(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab):}|=0`

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Without expanding the determinants 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):}|

Without expanding show that |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(2),-ab]|=0

Without expanding , show that |{:(x,a,x+a),(y,b,y+b),(z,c,z+a):}|=0

Without expanding show that |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

If a, b and c are all positive real, then prove that minimum value of determinant |{:(a^2+1,ab,ac),(ab,b^2+1,bc),(ac,bc,c^2+1):}| = 1+a^2+b^2+c^2

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

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

Prove that [[1,a,a^2 - bc],[1,b,b^2 - ca],[1,c,c^2 - ab]]

Using properties of determinants , prove that |{:(1,a,bc),(1,b,ca),(1,c,ab):}|=(a-b)(b-c)(c-a)

ARIHANT PUBLICATION-DETERMINANTS -CHAPTER PRACTICE
  1. If the determinant of matrix A of order 3 times 3 is of value 4, then ...

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  2. If f(x)|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}| then show that f(0)=0

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  3. Show that without expanding at any stage |{:(1/a,a^2,bc),(1/b,b^2,ca...

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  4. Find the area of triangle , whose vertices are (2,7) (1,1) and (10,8)

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  5. Show that the points (a+5,a-4),(a-2,a+3) and (a,a) do not lie on a st...

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  6. IF Ay is the cofactor of the element ay of the determinant |{:(2,-3,5)...

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  7. For what value of matrix [{:(6-x,4),(3-x,1):}] is a singular matrix?

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  8. For what value of x, A=[(2(x+1),2x),(x,x-2):}]singular matrix

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  9. Find x if [(1,2,x),(1,1,1),(2,1,-1):}]is singular

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  10. IF the value of the third order determinant is 12, then find the value...

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  11. IF for the non singular matrix A,A^2=I then find A^-1

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  12. A is a non singular symmetric matrix, write whether A^-1 is symmetric ...

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  13. Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

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  14. Prove that |[x, y, z],[x^2, y^2, z^2], [x^3, y^3, z^3]|=xyz(x-y)(y-z)(...

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  15. Prove the following : [[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]]-(5x+4)(4-x...

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  16. Prove that: |[1, 1+p, 1+p+q],[2, 3+2p, 1+3p+2p], [3, 6+3p, 1+6p+3q ]|=...

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  17. Without expanding the determinants prove that |{:(a,a^2,bc),(b,b^2,c...

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  18. IF a,b and c are in AP then find the value of the determinant |{:(x+2,...

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  19. Without expanding evaluate the determinant , |{:(sina,sinbeta,sin(a+d...

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  20. Prove that the determinant |{:(x, sin theta, cos theta),(-sin theta,...

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