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If AB= BA for any two square matrices ,...

If AB= BA for any two square matrices , then prove by mathematical induction that `(AB)^(n)=A^(n)B^(n)` .

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ARIHANT PUBLICATION-MATRICES -CHAPTER PRACTICE (Very Short Answer Type Questions)
  1. Let A=[{:(2,3),(-1,2):}]andf(x)=x^(2)-4x+7 . Show that f(A)=O. Use thi...

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  2. If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] , then find A^(2)-5A+6I.

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  3. If A=[{:(2,3),(1,2):}], then prove that A^(3)-4A^(2)+A=O.

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  4. If A=[{:(1,0),(-1,7):}], thenfind k such that A^(2)-8A+kI=O.

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  5. If A=[{:(3,-2),(4,-2):}], then find k such that A^(2)=kA-2I .

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  6. For the matrix A=[{:(3,1),(7,5):}] , find a and b such that A^(2)+aI...

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  7. Given that, A=[{:(4,0),(2k,5k):}] and B=[{:(k,0),(3,-1):}] such that A...

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  8. A factory makes three products P,Q and R .The table shows the units of...

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  9. A manufacturer sells the products x,y and z in two markets .Annual sal...

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  10. A trust fund has Rs. 35000 is to be invested in two different types o...

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  11. If AB= BA for any two square matrices , then prove by mathematical in...

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  12. If A = diag [{:(a,b,c):}] , then show that A^(n)="diag"[{:(a^(n),b...

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  13. If A=[{:(-1,2,3),(5,7,9),(-2,1,1):}]andB=[{:(-4,1,-5),(1,2,0),(1,3,1):...

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  14. FIND (1)/(2)(A+A')and(1)/(2)(A-A') , where A=[{:(0,a,b),(-a,0,c),(-b,...

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  15. Two shopkeepers A and B of a particular school have stock of books on ...

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  16. Three schools A ,B and C want to award their selected students for ...

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  17. If A=[{:(3,-4),(1,-1):}] , then show that (A-A') is a skew - symmetr...

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  18. Show that the matrix B^(T) AB is symmetric or skew -symmetric , acco...

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  19. Using elementary row transformation , find inverse of matrix A=[{:(6,...

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  20. Find the inverse of matrix A=[{:(1,2,4),(-1,-2,-1),(2,1,-1):}] by ele...

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