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

show that
`(i) [{:(5,-1),(6,7):}][{:(2,1),(3,4):}]ne[{:(2,3),(3,4):}][{:(5,-1),(6,7):}]`
`(ii) [{:(1,2,3),(0,1,0),(1,1,0):}][{:(-1,1,0),(0,-1,1),(2,3,4):}]`
`ne[{:(-1,1,0),(0,-1,1),(2,3,4):}][{:(1,2,3),(0,1,0),(1,1,0):}]`

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show that (i) [{:(5,-1),(6,7):}][{:(2,3),(3,4):}]ne[{:(2,3),(3,4):}][{:(5,-1),(6,7):}] (ii) [{:(1,2,3),(0,1,0),(1,1,0):}][{:(-1,1,0),(0,-1,1),(2,3,4):}] ne[{:(-1,1,0),(0,-1,1),(2,3,4):}][{:(1,2,3),(0,1,0),(1,1,0):}]

Show that (i) [(5,-1),(6,7)][(2,1),(3,4)]!=[(2,1),(3,4)][(5,-1),(6,7)] (ii) [(1,2,3),(0,1,0),(1,1,1)][(-1,1,0),(0,-1,1),(2,3,4)]!=[(-1,1,0),(0,-1,1),(2,3,4)][(1,2,3),(0,1,0),(1,1,0)] .

compute the indicated products . (i) [{:(a,b),(-b,a):}][{:(a,-b),(b,a):}](ii) [{:(1),(2),(3):}][2" "3 " "4 ] (iii) [{:(1,-2),(2,3):}][{:(1,2,3),(2,3,1):}] (iv)[{:(2,3,4),(3,4,5),(4,5,6):}][{:(1,-3,5),(0,2,4),(3,0,5):}] (V) [{:(2,1),(3,2),(-1,1):}][{:(1,0,1),(-1,2,1):}] (vi) [{:(3,-1,3),(-1,0,2):}][{:(2,-3),(1,0),(3,1):}]

Find AB and BA if exists from the following matrices A and B: (i) A=[{:(2,3,-1),(0,1,2):}]and B=[{:(2,-6),(-4,0):}] (ii) A=[{:(1,2,3),(0,1,-2),(-1,0,-1):}]and B=[{:(0,0,2),(2,0,0),(0,2,0):}] (iii) A=[{:(0,3,4),(2,1,-2),(1,-3,-1):}]and B=[{:(2,1,3),(-1,0,-2):}]

If P=[(0,1,0),(0,2,1),(2,3,0)],Q=[(1,2),(3,0),(4,1)] , find PQ.

Show that(i) [[5,-1],[ 6 ,7]][[2, 1],[ 3 ,4]]!=[[2, 1],[ 3, 4]][[5,-1],[ 6, 7]] (ii) [[1, 2, 3],[ 0, 1, 0],[ 1, 1, 0]][[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]]!=[[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]][[1 ,2 ,3],[ 0, 1, 0],[ 1, 1, 0]]

Verify that A(B+C)=(AB+AC), when (i) A=[{:(1,2),(3,4):}],B=[{:(2," "0),(1,-3):}]" and "C=[{:(1,-1),(0," "1):}]. (ii) A=[{:(2,3),(-1,4),(0,1):}],B=[{:(5,-3),(2," "1):}]" and "C=[{:(-1,2),(" "3,4):}].

Compute AB and BA, whichever exists when (i) A=[{:(2,-1),(3," "0),(-1," "4):}]" and "B=[{:(-2,3),(0,4):}] (ii) A=[{:(-1,1),(-2,2),(-3,3):}]" and "B=[{:(" "3,-2," "1),(" "0," "1," "2),(-3," "4,-5):}] (iii) A=[{:(0,1,-5),(2,4," "0):}]" and "B=[{:(1,3),(-1,0),(0,5):}] (iv) A=[1" "2" "3" "4]" and "B=[{:(1),(2),(3),(4):}] (v) A=[{:(2,1),(3,2),(-1,1):}]" and "B=[{:(1,0,1),(-1,2,1):}]

Find the inverse of the following matrices if exist : (i) |{:(5,-3),(2,2):}| (ii) |{:(1,-3),(-1,2):}| (iii) |{:(1,0,-1),(3,4,5),(0,-6,-7):}| (iv) |{:(1,-3,3),(2,2,-4),(2,0,2):}| (v) |{:(1,2,1),(1,-1,-2),(1,2,-1):}| (vi) |{:(4,-2,-1),(1,1,-1),(-1,2,4):}|

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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