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If F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(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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NCERT TAMIL-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)] and C=[(...

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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,sin theta),(-sintheta,costheta)]+sin[(sint...

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

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  6. Find X, if Y=[(3,2),(1,4)] and 2X+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),(0,2...

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  9. If x[(2),(3)]+y[(-1),(1)]=[(10),(5)], find the value of x and y.

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  10. Given 3[(x,y),(z,w)]=[(x,6),(-1,2w)]+[(4,x+y),(z+w,3)], find the value...

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

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

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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)], prove that A^(3)-6A^(2)+7A+2I=0

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

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  16. If A=[(0,-"tan"(alpha)/(2)),("tan"(alpha)/(2),0)] and I is the identit...

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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 do...

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  19. Assume X, Y, Z, W and P are matrices of order 2xx n, 3xxk, 2xxp, n xx...

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  20. Assume X, Y, Z, W and P are matrices of order 2xx n, 3xxk, 2xxp, n xx...

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