Question: linear algebra question Let us consider the linear transformation T : RS -> RS defined as follows: T(x) is obtained from x = ($1, 12,

linear algebra question

Let us consider the linear transformation T : RS -> RS defined as follows: T(x) is obtained from x = ($1, 12, 13) by . first rotating the vector of its first two components (71, 12) by an angle of 0 E (0, 7/2) in the counter clock-wise direction leaving 23 unchanged, . then applying a transformation that maps (21, 22, 23) E RS to (21, 22 + 223, 23-322) C R3. Find the standard matrix of T. Is this transformation one-to-one? Is it onto? Explain

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