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If A(alpha)=[{:(cosalpha,sinalpha),(-sin...

If `A_(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}]`, then prove that `A_(alpha)A_(beta)=A_(alpha+beta)`.

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ARIHANT PUBLICATION-MATRICES -CHAPTER PRACTICE (Very Short Answer Type Questions)
  1. How many different matrix products can you form with these three matri...

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  2. Solve the matrix [{:(x,-5,-1):}][{:(1,0,2),(0,2,1),(2,0,3):}][{:(x),(4...

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  3. If A(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}], then prove...

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  4. If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] , then find the va...

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  5. If [{:(2,1,3):}][{:(-1,0,-1),(-1,1,0),(0,1,1):}][{:(1),(0),(-1):}]=A ...

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  6. Find the matrix A satisfying the equation [{:(2,1),(3,2):}].A.[{:(-3...

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  7. If A=[{:(1,0,2),(0,2,1),(2,0,3):}], then prove that A is a root of th...

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  8. Let A=[{:(2,3),(-1,2):}]andf(x)=x^(2)-4x+7 . Show that f(A)=O. Use thi...

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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