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Simplify: cos theta[{:(costheta,sinthe...

Simplify:
`cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]`

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`cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]`
`=[{:(cos^(2)theta,sinthetacostheta),(-sintheta, costheta):}]+[{:(sin^(2)theta,-sinthetacostheta),(sinthetacos theta,sin ^(2)theta):}]`
`=[{:(cos^(2)theta+sin^(2)theta,sinthetacos theta -sin theta cos theta ),(-sin thetacos theta +sintheta cos theta, cos^(2)theta +sin^(2)theta):}]`
`[{:(1,0),(0,1):}]`
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NAGEEN PRAKASHAN-MATRICES-Exercise 3.2
  1. compute the indicated products . (i) [{:(a,b),(-b,a):}][{:(a,-b),(b,...

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

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  4. Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+si...

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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) 2X+3Y=[2 3 4 0]...

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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]=3[3 5 4...

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

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  10. 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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  11. If f(x) = [(cos x , - sinx,0),(sinx,cosx,0),(0,0,1)] then show f(x) . ...

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

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  13. If f(x)=x^2-5x+6. Find f(A),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 A=[3-2 4-2]and I=[1 0 0 1], find k so that A^2=k A-2I.

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

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  17. A trust fund has Rs. 30000 that must be invested in two different t...

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

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  19. the restriction on n, k and p so that PY +Wywill be defined are :

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  20. If n" "=" "p , then the order of the matrix 7X" "" "5Z is: (A) p xx...

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