InterviewSolution
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InterviewSolution
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If `[[cos theta,sin theta],[-sin theta,cos theta]], ` then `lim _(n rarr infty )A^(n)/n ` is (where `theta in R`)A. a zero matrixB. an identity matrixC. `[[0,1],[-1,0]]`D. `[[0,1],[0,-1]]` |
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Answer» Correct Answer - A `because A = [[cos theta , sin theta],[-sin theta, cos theta ]]` `therefore A^(n) = [[cos ntheta , sin ntheta],[-sin ntheta, cos ntheta ]]` `rArr A^(n)/n = [[lim_(nrarr infty)(cos ntheta)/n , lim_(nrarr infty)(sin ntheta)/n],[-lim_(nrarr infty)(sin ntheta)/n, lim_(nrarr infty)(cos ntheta)/n ]]= [[0,0],[0,0]]` = a zero matirx `[because - 1 lt sin infty 1 and -1 lt cos infty lt 1]` |
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