Let rx: R3 → R3 be the linear transformation which rotates counter-clockwise around the x-axis by an angle of π/4 radians
Let rx: R3 → R3 be the linear transformation which rotates counter-clockwise around the x-axis by an angle of π/4 radians. Similarly, let ry be the rotation by an angle of π/4 radians around the y axis.
(a) Find the standard matrices for rx and ry
(b) Find the standard matrix for rx o ry
(c) Find the standard matrix for ry o ry
Homework Answers
Given, 
is the linear transformation which rotates counter-clockwise
around the x-axis by an angle of 
radians.
And, 
is the linear transformation which rotates counter-clockwise
around the y-axis by an angle of radians.
a) Now, Ax = 
i.e., Ax = 
And, Ay = 
i.e., Ay = 
Therefore, standard matrix for rx is
and standard matrix for ry is
.
b) Now, Ax*Ay =
= 
Therefore, standard matrix for 
is
.
c) Now, Ay*Ax =
= 
Therefore, standard matrix for 
is
.
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Let rx: R3 → R3 be the linear transformation which rotates counter-clockwise around the x-axis by an angle of π/4 radians
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