Consider matrix A = Then which one of the following is true ? Note that p...

 

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Consider matrix A = Then which one of the following is true ? Note that p (A) is spectral radius of A. lim, || A" ||= 0 for all natural norms, p(A) <1 and lim, A"x = 0 for any x in R". lim,co || A" ||= 0 for all natural norms, p(A) > 1 and lim,- -o A"x = 0 for any x such that ||x|| = 1 in R". limn00 I| A" 0 for all natural norms, lim,o [p (A)]" = 0 and %3D lim- A"x + 0 for some x and ||x|| = 1 in R". 00 lim,. I| A" ||= 0 for all natural norms, p (A) = 1 and lim, . A"x = 0 for any x such that ||x|| = 1 in R". %3D %3! O -Im Consider matrix A = Then which one of the following is true ? Note that p (A) is spectral radius of A. lim, || A" ||= 0 for all natural norms, p(A) <1 and lim, A"x = 0 for any x in R". lim,co || A" ||= 0 for all natural norms, p(A) > 1 and lim,- -o A"x = 0 for any x such that ||x|| = 1 in R". limn00 I| A" 0 for all natural norms, lim,o [p (A)]" = 0 and %3D lim- A"x + 0 for some x and ||x|| = 1 in R". 00 lim,. I| A" ||= 0 for all natural norms, p (A) = 1 and lim, . A"x = 0 for any x such that ||x|| = 1 in R". %3D %3! O -Im