Write down the matrices representing the linear transformations f satisfying the fol- lowing properties: (a) f(e1) = and f(e,) = || (b) f reflects R² in the line Y (c) f reflects R² in the y-axis then rotates the plane anticlockwise by an angle 0. = -x.

Elementary Linear Algebra (MindTap Course List)
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 17CM
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3. Write down the matrices representing the linear transformations f satisfying the fol-
lowing properties:
(a) f(e1) =
2
and f(e2) = i
2
(b) ƒ reflects R² in the line y
(c) f reflects R² in the y-axis then rotates the plane anticlockwise by an angle 0.
= -x.
Transcribed Image Text:3. Write down the matrices representing the linear transformations f satisfying the fol- lowing properties: (a) f(e1) = 2 and f(e2) = i 2 (b) ƒ reflects R² in the line y (c) f reflects R² in the y-axis then rotates the plane anticlockwise by an angle 0. = -x.
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