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Let F(alpha)={:[(cosalpha,-sinalpha,0),(...

Let `F(alpha)={:[(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1)] and G(beta) = [(cosbeta,0,sinbeta),(0,1,0),(-sinbeta,0,cosbeta)]`. Show that `[F(alpha).G(beta)]^-1=G(-beta),F(-alpha)`

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Let F(alpha)={:[(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1)] ...

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  2. Let A be a square matrix of order 3xx3, then prove that |kA|=k|A|.

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  3. If any two rows (or columns) of a determinant are identical, the value...

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  4. Answer in one word. {:|(3,1,6),(5,2,10),(7,4,14)|

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  5. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

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  6. Write the value of the following determinant abs{:(a-b, b-c, c-a),(b-c...

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  7. Use properties of determinants ot evaluate: {:|(2,a,abc),(2,b,bca),(...

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  8. Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y)...

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  9. Evaluate |[102,18,36],[1,3,4],[17,3,6]|

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  10. Use properties of determinants ot evaluate: {:|(2,3,1),(4,6,2),(1,3,...

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  11. Use properties of determinants ot evaluate: {:|(2,3,5),(261,592,127)...

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  12. Show that x=1 is a root of the equation: {:|(x+1,2x,-11),(2x,x+1,-4...

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  13. If p,q,r ar in A.P. write the value of : {:|(x+1,x+2,x+2p),(x+2,x+3,...

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  14. Without expanding, prove that the following determinant vanishes. |...

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  15. Without actual expansion, prove that the following determinants vanish...

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  16. Without actual expansion, prove that the following determinants vanish...

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  17. Without actual expansion, prove that the following determinants vanish...

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  18. Without actual expansion, prove that the following determinants vanish...

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  19. Without actual expansion, prove that the following determinants vanish...

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  20. Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x ,...

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  21. Without expanding, prove that : |{:(1, bc, a(b+ c) ),(1, ca, b ( c+ a)...

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