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If A=[1 0-1 7] and I=[1 0 0 1] , then fi...

If `A=[1 0-1 7]` and `I=[1 0 0 1]` , then find `k` so that `A^2=8A+k I`

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The correct Answer is:
`K=-7`
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MODERN PUBLICATION-MATRICES-Exercise 3 (d ) Short Answer Type Questions
  1. If P=[(0,1,0),(0,2,1),(2,3,0)],Q=[(1,2),(3,0),(4,1)], find PQ.

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  2. If I is the identity matrix and A is a square matrix such that A...

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  3. If A=[1 0-1 7] and I=[1 0 0 1] , then find k so that A^2=8A+k I

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  4. if A=[{:(costheta,sin theta ),(-sin theta,costheta):}], then show that...

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  5. If A=[(2,-3,1),(-2,3,4)] and B=[(2,5),(3,1),(4,2)], then Find AB

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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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