Question: The norm of a linear transformation TA: Rn Rn can be defined by where the maximum is taken over all nonzero x in Rn. (The

The norm of a linear transformation TA: Rn †’ Rn can be defined by

where the maximum is taken over all nonzero x in Rn. (The subscript indicates that the norm of the linear transformation on the left is found using the Euclidean vector norm on the right.) It is a fact that the largest value is always achieved-that is, there is always some x0 in Rn such that ||T||E = max(||T(x0)|| / ||x0||). What are the norms of the linear transformations TA with the following matrices?
(a)

(b)

(c)

(d)

11271 E = max-11T(x) 11 11 0 1 2 0 2 /2 3

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