Question

Suppose R: |R^2 -> |R^2 is the linear transformation:

R( x1 , x2) = (x2 , x1)

a) Give a geometric description of R.

b) Compute the matrix of R relative to te standard basis of |R^2

c) Let v1 = (1, 1) and v2 = (1, -1)

Verify that B = (v1, v2) is a basis for |R^2, and compute the matrix of R relative to the basis B, i.e [R]B

Answer 1

Please find the attached files for the solution. Notation: B_std stands for the standard basis {e1, e2} of IR^2.

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