Description
Let 𝑇 be the linear transformation of reflection across the plane 𝑃 of 𝑥1-2𝑥2=0. To
make it easy to find the transformation matrix, consider the following two spaces of 𝑉=𝑅3 and
𝑊=𝑅3 whose bases are given by
{[𝑥1𝑥2𝑥3]=[100],[010],[001]} and {[210],[001],[-120],}
respectively.
(a) (10) Find the matrix 𝐵 representing the linear transformation of 𝑇 with respect to the
basis of 𝑊.
(b) (10) Find the matrix 𝑀 for the change of basis from 𝑊 to 𝑉.
(c) (15) Find the matrix A representing the linear transformation of 𝑇 with respect to the basis
of 𝑉.
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