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Prove that the determinant |{:(x, sin ...

Prove that the determinant
`|{:(x, sin theta, cos theta),(-sin theta,-x,1),(cos theta,1,x):}|` is independent of `theta`

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ARIHANT PUBLICATION-DETERMINANTS -CHAPTER PRACTICE
  1. Without expanding the determinants prove that |{:(a,a^2,bc),(b,b^2,c...

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

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

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

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

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

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

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

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  9. Evaluate |{:(1,1,1),(nC1,n+2C1,n+4C1),(nC2,n+2C2,n+4C2):}|

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  10. Find the values of k, if the area of traingle is 4sq units and vertice...

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  11. Show that the points A(a,b+c), B(b,c+a) and C(c,a+b) are collinear.

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  12. IF A=[(1,3,3),(1,4,3),(1,3,4):}] then find |A|

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  13. Find the inverse of the matrixA=[(a,b),(c,(1+bc)/a):}] and show that a...

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  14. If A=[(2,2,1),(-2,1,2),(1,-2,2):}] and B=[(1,3,2),(1,1,1),(2,-3,1):}] ...

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  15. If F(alpha)=[(cos a,-sina,0),(sina,cosa,0),(0,0,1):}]andG(beta)=[(cosb...

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  16. Using matrices solve the following system of equations 4x+3y+2z=60,x+2...

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  17. If A=[[1,-2,1],[0,-1,1],[2,0,-3]]then find A^(-1) and hence solve the ...

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  18. If A=[(3,-4,2),(2,3,5),(1,0,1):}] then find A^-1 and hence solve the f...

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  19. IFA=[(2,-1,1),(-1,2,-1),(1,-1,2):}]and B=[(3,1,-1),(1,3,1),(-1,1,3):}]...

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  20. IF A=[(1,-2,0),(2,1,3),(0,-2,1):}]and B=[(7,2,-6),(-2,1,-3),(-4,2,5):}...

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