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If F(x)=[{:(cosx,-sinx,0),(six,cosx,0),(...

If `F(x)=[{:(cosx,-sinx,0),(six,cosx,0),(0,0,1):}]`, show that `F(x).F(y)=F(x+y).`

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The correct Answer is:
`F(x+y)`.
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MODERN PUBLICATION-MATRICES-NCERT - FILE (Question from NCERT Book) (Exercise 3.2)
  1. A=[{:(2,4),(3,2):}],B=[{:(1,3),(-2,5):}],C=[{:(-2,5),(3,4):}] find ...

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  2. compute the following : (i) [{:(a,b),(-b,a):}]+[{:(a,b),(b,a):}] (...

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  3. Compute the indicated products (i) [(a,b),(-b,a)][(a,-b),(b,a)] (...

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  4. if A=[{:(1,2,-3),(5,0,2),(1,-1,1):}],B=[{:(3,-1,2),(4,2,5),(2,0,3):}]a...

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  5. A=[[2/3,1,5/3],[1/3,2/3,4/3],[7/3,2,2/3]] and B=[[2/5,3/5,1],[1/5,2/5,...

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  6. costheta[{:(costheta,-sin theta),(sintheta,costheta):}]+sintheta[{:(si...

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  7. Find X and Y, if(i) X+Y=[7 0 2 5]and X-Y=[3 0 0 3](ii) 2X+3Y=[2 3 4 0]...

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  8. Find X if Y=[3 2 1 4] and 2X+Y=[1 0-3 2] .

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  9. Find X and Y,if 2[{:(1,3),(0,x):}]+[{:(y,0),(1,2):}]=[{:(5,6),(1,8...

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  10. Find x ,\ y ,\ z ,\ t if 2[x z y t]+3[1-1 0 2]=3[3 5 4 6] .

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  11. If x[2 3]+y[-1 1]=[10 5] , find the values of x and y.

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  12. Given 3[x y z w]-[x6-1 2w]+[4x+y z+w3] , find the values of x, y, z an...

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  13. If F(x)=[{:(cosx,-sinx,0),(six,cosx,0),(0,0,1):}], show that F(x).F(y)...

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  14. Show that (i) [(5,-1),(6,7)][(2,1),(3,4)]!=[(2,1),(3,4)][(5,-1),(6,7...

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  15. Find A^2-5A+6I , if A=[2 0 1 2 1 3 1-1 0]

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  16. If A=[1 0 2 0 2 1 2 0 3] , prove that A^3-6A^2+7A+2I=0

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  17. If A=[(3,-2),(4,-2)] and I=[(1,0),(0,1)], find k so that A^(2)=kA-2I.

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  18. Let A=[0-tan(alpha//2)tan(alpha//2)0] and I be the identity matrix ...

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  19. A trust fund has Rs 30,000 that must be invested in two different t...

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  20. The bookshop of a particular school has 10 dozen chemistry books, 8...

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