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Let A = [(1,0),(2,3)] and A^(n) = [(a, b...

Let `A = [(1,0),(2,3)] and A^(n) = [(a, b),(c,d)]` then `lim_(n to oo) (b + c)/(a + d)` =

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The correct Answer is:
1
`A = [(1,0),(2,3)], A^2 = [(1,0),(2 + 2 xx 3, 3^2]`
`A^3 = [(1,0),(2+2xx3+2xx3^2,3^3)]`
Hence `A^(n) = [(1,0),(2+2xx3+....+2xx3^(n-1),3^n)]= [(a,b),(c,d)]`
`implies lim_(n to oo) (b + c)/(a + d) = lim_(n to oo)(2 + 2 xx 3 + 2 xx 3^2 + ……+ 2 xx 3^(n-1))/(1 + 3^n) = lim_(n to oo) (3^(n) - 1)/(3^n + 1) = 1`.
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