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If A=[{:(3,-4),(1,-1):}] then show that ...

If `A=[{:(3,-4),(1,-1):}]` then show that `A^(k)=[{:(1+2k,-4k),(k,1-2k):}],k epsilon N`

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ARIHANT PUBLICATION-MATRICES -QUESTIONS FPR PRACTICE Part II (Multiplication of Matrices (Matrix Multiplecation) Short Answer Type Questions
  1. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  2. If A and B are square matrices of same order, then show by means of an...

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  3. Find the product [{:(1,2,3),(2,3,4):}][{:(1,-2),(-2,3):}]

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

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  5. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  6. Find x, so that [{:(1,x,1):}][{:(1,3,2),(0,5,1),(0,3,2):}][{:(1),(1),(...

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  7. Find the matrix A such that A[{:(1,2,3),(4,5,6):}]=[{:(-7,-8,-9),(2,4...

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  8. If the matrix A is such that [{:(1,-1),(2,3):}]A=[{:(-4,1),(7,7):}] th...

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  9. Let A=[{:(2,-1),(3,4):}],B=[{:(5,2),(7,4):}]andC=[{:(2,5),(3,8):}]. F...

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  10. If f(x)=[{:(cosx,-sinx,0),(sinx,cosx,0),(0,0,1):}], then show that ...

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  11. If A= [{:(1,-1),(2,-1):}],B=[{:(a,1),(b,-1):}]and(A+B)^(2)=A^(2)+B^(2)...

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  12. If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]] show that (I+A) =(I-A)[[c...

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  13. To promote the making of toilets for women , an organisation tried to ...

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  14. There are threee families A , B and C . The number of men , women and ...

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  15. In a parliament election , a political party hired a public relation...

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  16. There are two families A and B . There are 4 men , 6 women and 2 child...

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