LetA= 0 2 0 .
101
(a) (5 points) Show
that A2 − 2A = O, where O is the
zero matrix.
(b) (5 points) Show
that An − 2An−1 = O for any positive
integer n ≥ 2.
(c) (5 points) Is A invertible? If true,
calculate A−1; otherwise, calculate (A + I)−1,
where I is the
Leta 0 2 0 101 A 5 Points Show That A2 2a O Where O Is The Zero Matrix B 5 Points Show That An 2a 1 (196.44 KiB) Viewed 23 times
1. (15 points) Let A= - [ 1 0 1 0 2 0 1 0 1 = 2 n - = (a) (5 points) Show that A2 – 2A = 0, where O is the zero matrix. (b) (5 points) Show that A" – 2A-1 = 0 for any positive integer n > 2. O (c) (5 points) Is A invertible? If true, calculate A-1; otherwise, calculate (A + I)-7, where I is the 3 x 3 identify matrix.
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