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If A=[[costheta,-sintheta],[sintheta,cos...

If `A=[[costheta,-sintheta],[sintheta,costheta]]` then show that `A^n = [[cosntheta,-sinntheta],[sinntheta,cosntheta]]`

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MODERN PUBLICATION-MATRICES-Exercise 3 (d) Long Answer Type Questions I
  1. If A=[3 1-1 2] , show that A^2-5A+7I=O . Use this to find A^4

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  2. Let A ={:[(2,0,1),(2,1,3),(1,-1,0)] and f(x) = x^(2) -5x + 6 , find f(...

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  3. यदि A= [[2,0,1],[2,1,3],[1,-1,0]], तब A^(2) - 3A + 2I का मान ज्ञात क...

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  4. if A=[{:(3,1),(-1,2):}],show that A^(2)-5A+7I=0.

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  5. If M=[(7,5),(2,3)], then verify the equation : M^(2)-10M+11I(2)=O

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  6. If A+l={:[(2,2,3),(3,-1,1),(4,2,2)]:} then show that A^(3)-23A-40l=0

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  7. If A=[1 0 2 0 2 1 2 0 3] , prove that A^3-6A^2+7A+2I=0

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  8. If A=[{:(-1,2),(3,1):}], find f(A), where f(x)=x^(2)-2x+3.

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  9. If A=[(3,1),(-1,2)], then find f (A), where f(x)=x^(2)-5x+7.

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  10. If A=[1 0-1 7] , find k such that A^2-8A+k I=O .

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  11. If A A=[3-2 4-2]and I=[1 0 0 1], find k so that A^2=k A-2I.

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  12. If A=[(0,3),(-7,5)] and I=[(1,0),(0,1)], then find 'k' so that k^(2)=5...

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  13. Solve system of linear equations, using matrix method, x y" "+" "2...

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  14. Let A=[0 1 0 0]show that (a I+b A)^n=a^n I+n a^(n-1)b A, where I is t...

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  15. A matrix X has a+b rows and a+2 columns while the matrix Y has b+1 ...

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  16. Let A=[(-1,-4),(1,3)], prove by Mathematical Induction that A^(n)=[(1-...

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  17. If A=[[costheta,-sintheta],[sintheta,costheta]] then show that A^n = [...

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  18. If A=[costhetaisinthetaisinthetacostheta], then prove by principal of ...

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  19. A trust fund has Rs 30,000 that must be invested in two different t...

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  20. There are 2 families A and B. There are 4 men, 6 women and 2 children ...

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