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Three matrices A,Band C defined as A=[{:...

Three matrices A,Band C defined as `A=[{:(1,2),(-1,3):}],B=[{:(4,0),(1,5):}]andC=[{:(2,0),(1,-2):}]`, then show that matrices A,B and C satisfy
(i) the property of associativity with respect to multiplication ,i.e A(BC)=(AB)C.
(ii) the property of distributivity with respect to addition i.e A(B+C)=AB+AC.

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`thereforeLHS=RHS`
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ARIHANT PUBLICATION-MATRICES -CHAPTER PRACTICE (Very Short Answer Type Questions)
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  7. If Possible , then find the sum of the matrices A and B , where A=[{:(...

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  8. Simplify[{:(cos^(2)x,sin^(2)x),(sin^(2)x,cos^(2)x):}]+[{:(sin^(2)x,cos...

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  11. Solve for x and y , x [{:(2),(1):}]+y[{:(3),(5):}]=[{:(-8),(-11):}]

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  12. If A=[{:(2,4),(3,2):}]andB=[{:(1,3),(-2,5):}], then find A-B.

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  13. If [{:(9,-1,4),(-2,1,3),(1,2,-1):}]=A+[{:(1,2,-1),(0,4,9),(3,1,-2):}] ...

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  14. Assume Y, W and P are the matrices of orders 3xxk,nxx3andpxxk .Find t...

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  15. Let A=[a(ij)](nxxn) be a diagonal matrix whose diagonal elements are...

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  17. Find x from the matrix equation [{:(1,3),(4,5):}][{:(x),(2):}]=[{:(5)...

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  18. If matrix A=[{:(1,-1),(-1,1):}]andA^(2)=kA , then write the value of k...

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  19. Show by an example that for AneO,BneOandAB=O.

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  20. If A=[{:(1,2),(3,4):}]then find A+A .

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  21. If A=[{:(0,-1,2),(4,3,-4):}]andB=[{:(4,0),(1,3),(2,6):}] then verify t...

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