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94 Chapter 3 Matrix Algebra
Exercises for section 3.4
Each problem in this section concerns the following three linear transformations
2
in .
f(p)
Rotation: Rotate points counterclockwise
through an angle θ. θ p
Reflection: Reflect points about the x -axis.
p
f(p)
y = x
p
Projection: Project points onto the line
y = x in a perpendicular f(p)
manner.
3.4.1. Determine the matrix associated with each of these linear functions.
That is, determine the a ij ’s such that
x 1 a 11 x 1 + a 12 x 2
f(p)= f = .
x 2 a 21 x 1 + a 22 x 2
3.4.2. By using matrix multiplication, determine the linear function obtained
by performing a rotation followed by a reflection.
3.4.3. By using matrix multiplication, determine the linear function obtained
by first performing a reflection, then a rotation, and finally a projection.
