a) Find a matrix P that diagonalizes A and determine 𝑷
−𝟏𝑨𝑷, where
𝑨 = (
𝟐 −𝟏 𝟎 𝟎
−𝟐 𝟑 𝟎 𝟎
𝟐 𝟎 𝟒 𝟐
𝟏 𝟑 −𝟐 −𝟏
)
b) Let L denote the linear transformation in ℝ𝟐 which describes a reflection in
ℝ𝟐
about the line 𝒙𝟐 = 𝒙𝟏. Find the matrix of A and its eigenvalues and
eigenvectors.
c) The matrix of a linear transformation T on ℝ𝟑
relative to the usual basis
{𝒆𝟏 = (𝟏, 𝟎,𝟎), 𝒆𝟐 = (𝟎,𝟏, 𝟎), 𝒆𝟑 = (𝟎,𝟎, 𝟏)} is [
𝟎 𝟏 𝟏
𝟏 𝟎 −𝟏
−𝟏 −𝟏 𝟎
]. Find the
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