a. Prove that
||x(k) − x|| ≤ ||T||k ||x(0) − x|| and ||x(k) − x|| ≤ ||T||k /1 − ||T|| ||x(1) − x(0) ||,
Where T is an n × n matrix with ||T|| < 1 and
x(k) = Tx(k−1) + c, k = 1, 2, . . . ,
With x(0) arbitrary, c ∈ Rn, and x = Tx + c.
b. Apply the bounds to Exercise 1, when possible, using the l∞ norm.
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