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

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

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KUMAR PRAKASHAN-MATRICES -EXERCISE -3.2
  1. Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (i...

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  2. 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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  3. If A=[{:((2)/(3),1,(5)/(3)),((1)/(3),(2)/(3),(4)/(3)),((7)/(3),2,(2)/(...

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  4. Simplify : costheta[{:(costheta,sintheta),(-sintheta,costheta):}]+s...

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

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  6. Find X , if Y=[{:(3,2),(1,4):}]and2X+Y=[{:(1,0),(-3,2):}].

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

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  8. Solve the equation for x,y,z and t,if 2[{:(x,z),(y,t):}]+3[{:(1,-1),(0...

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  9. If x[{:(2),(3):}]+y[{:(-1),(1):}]=[{:(10),(5):}], find thevalues of x ...

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  10. Given 3[{:(x,y),(z,w):}]=[{:(x,6),(-1,2w):}]+[{:(4,x+y),(z+w,3):}], fi...

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

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  12. Show that (i) [{:(5,-1),(6,7):}][{:(2,1),(3,4):}]ne[{:(2,1),(3,4):}]...

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  13. Find A^(2)-5A+6I, if A=[{:(2,0,1),(2,1,3),(1,-1,0):}].

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  14. If A=[{:(1,0,2),(0,2,1),(2,0,3):}] then , prove that A^(3)-6A^(2)+7...

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  15. If A=[{:(3,-2),(4,-2):}]andI=[{:(1,0),(0,1):}], find k so that A^(2)=...

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  16. If A=[{:(0,"tan"(alpha)/(2)),("tan"(alpha)/(2),0):}]and I theidentity ...

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

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

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  19. Assume X, Y, Z, W and P Are Matrices of Order 2 x n, 3 x k, 2 x p, n x...

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  20. Assume X, Y, Z, W and P Are Matrices of Order 2 x n, 3 x k, 2 x p,N x ...

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