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if A=[{:(costheta,sin theta ),(-sin thet...

`if A=[{:(costheta,sin theta ),(-sin theta,costheta):}]`, then show that :
`A^(2)=[{:(cos2hetha,sin2theta),(-sin2theta,cos2theta):}]`

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if A=[{:(costheta,sin theta ),(-sin theta,costheta):}] , then show that : A^(2)=[{:(cos2theta,sin2theta),(-sin2theta,cos2theta):}]

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If A=[[cos 2 theta, sin 2 theta],[-sin2theta, cos2theta]] , find A^2

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Let triangle1=|{:(x,sintheta,costheta),(-sintheta,x,1),(costheta,1,x):}| and triangle2=|{:(x,sin2theta,cos2theta),(-sin2theta,x,1),(cos2theta,1,x):}| then which of following is/are true?

MODERN PUBLICATION-MATRICES-Exercise 3 (d ) Short Answer Type Questions
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  6. If A=[(1,-2,3),(-4,2,5)] and B=[(2,3),(4,5),(2,1)], find AB and BA and...

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  7. यदि A = [{:(5,-1),(6,7)]"ओर " B = [ {:(2,1),(3,4):}] तो सिद्ध कर...

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  8. Evaluate the following : (i) [(4),(5)][7" "9]+[(4,0),(0,-5)] (ii)...

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  9. If [ (2x, 3)] [(1,2),(-3,0)][(x),(8)]=0, find 'x'

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  10. for what values of x: [1" "2" "1][{:(1,2,0),(2,0,1),(1,0,2):}][{:(...

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  11. find x, if [x" "-5" "-1][{:(1,0,2),(0,2,1),(2,0,3):}][{:(x),(4),(1)...

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  12. Find the values of 'a' and 'b' for which the following hold : [(3,2)...

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  13. Let A=[(2,4),(1,-3)] and B=[(1,-1,5),(0,2,6)] (a) Find AB. (b) Is BA...

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  14. If A=[(1,-2,3),(-4,2,5)] and B=[(2,3),(4,5),(2,1)], find AB and BA and...

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  15. Show that AB = BA in each of the following cases: (i) A=[{:(costheta...

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

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  17. Show with the help of an example that AB=O whereas BA!=O, where O is a...

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  18. Give an example of three matrices A ,\ B ,\ C such that A B=A C but...

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  19. If A=[(5,2),(-1,2)] and I=[(1,0),(0,1)] show that : (A-3I)(A-4I)=O

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  20. If A=[(2,0,1),(2,1,3),(1,-1,0)], then find (A^(2)-5A)

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