Problem

Find the standard matrix representation for each of the following linear operators:...

Find the standard matrix representation for each of the following linear operators:

(a) L is the linear operator that rotates each x in R2 by 45? in the clockwise direction.

(b) L is the linear operator that reflects each vector x in R2 about the x1-axis and then rotates it 90? in the counterclockwise direction.

(c) L doubles the length of x and then rotates it 30? in the counterclockwise direction.

(d) L reflects each vector x about the line x2 = x1 and then projects it onto the x1-axis.

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Solutions For Problems in Chapter 4.2