Purchase Solution

Working with Rotational Matrices

Not what you're looking for?

Ask Custom Question

R is a 3x3 matrix. What property is required of R for it to be an orthogonal matrix. and (I:-) a rotation matrix? Write down the matrix that effects a rotation by angle theta about the y-axis.

See attachment for the rest of the questions.

Attachments
Purchase this Solution

Solution Summary

This provides an example of how to work with rotational matrices in an attachment. The matrix effects on rotation by angle theta about the y-axis is determined.

Solution Preview

Please see the attached file.

Question1:
(a) A 3 x 3 matrix R is an orthogonal matrix is RRt = RtR = I, i.e., its transpose is its inverse.
(b) A 3 x 3 matrix R is a rotation matrix if in addition to being an orthogonal matrix, its determinant is equal to +1.
i.e., RRt = RtR = I and det(R) = 1
The 3 x 3 rotation matrix is:

Question2:
b = M.a
Premultiplying ...

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.