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The set of natural numbers is divided in...

The set of natural numbers is divided into array of rows and columns in the form of matrices as `A_(1)=[1], A_(2)=[(2,3),(4,5)], A_(3)=[(6,7,8),(9,10,11),(12,13,14)]` and so on. Let the trace of `A_(10)` be `lambda` . Find unit digit of `lambda` ?

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The correct Answer is:
`(n)/(6)[2n^(3)+n+3]`
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MOTION-MATRICES -Exercise - 4 (Level-II)
  1. The set of natural numbers is divided into array of rows and columns i...

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  2. Let A=[1 0 0 0 1 1 0-2 4],I=[1 0 0 0 1 0 0 0 1]a n dA^(-1)=[1/6(A^2+c ...

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  3. If P=[[sqrt3/2,1/2] , [-1/2,sqrt3/2]] and A=[[1,1] , [0,1]] and Q=PAP^...

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  4. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

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  5. Let A = [(1,0,0), (2,1,0), (3,2,1)], and U1, U2 and U3 are columns of ...

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  6. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

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  7. Match the following {:("(A) The minimum value of "(x^(2)+2x+4)/(x+2)...

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  8. Let A be the set of all 3 xx 3 symmetric matrices all of whose entrie...

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  9. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  10. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  11. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

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  12. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

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  13. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

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  14. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

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  15. Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-...

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  16. Let M be a 3xx3 matrix satisfying M[{:(0),(1),(0):}]=[{:(-1),(2),(3):}...

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  17. Let P = [a(ij)] " be a " 3 xx 3 matrix and let Q = [b(ij)], " where " ...

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  18. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

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  19. If the adjoint of a 3 3 matrix P is 1 4 4 2 1 7 1 1 3 , then the po...

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  20. For 3xx3 matrices Ma n dN , which of the following statement (s) is (a...

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  21. Let Ma n dN be two 3xx3 matrices such that M N=N Mdot Further, if M!=N...

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