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For what value of matrix [{:(6-x,4),(3-x...

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

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ARIHANT PUBLICATION-DETERMINANTS -CHAPTER PRACTICE
  1. 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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  2. IF Ay is the cofactor of the element ay of the determinant |{:(2,-3,5)...

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

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

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

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

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

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

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  9. 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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  10. 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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  11. Prove the following : [[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]]-(5x+4)(4-x...

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

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

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

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

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

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  17. Using properties of determinants evaluate |{:(0,ab^2,ac^2),(a^2b,0,b...

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  18. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

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  19. Using properties of determinats show that |{:(a,a+b,a+2b),(a+2b,a,a+b)...

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  20. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

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