Chapter 3: Q13-18P (page 179)
Show that division cannot be a group operation. Hint: See (13.7 d).
Division is not a group operation
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
A particle is traveling along the line (x-3)/2=(y+1)/(-2)=z-1. Write the equation of its path in the form . Find the distance of closest approach of the particle to the origin (that is, the distance from the origin to the line). If t represents time, show that the time of closest approach is . Use this value to check your answer for the distance of closest approach. Hint: See Figure 5.3. If P is the point of closest approach, what is ?
Find the Eigen values and eigenvectors of the following matrices. Do some problems by hand to be sure you understand what the process means. Then check your results by computer.
Question: Verify that each of the following matrices is Hermitian. Find its eigenvalues and eigenvectors, write a unitary matrix U which diagonalizes H by a similarity transformation, and show that is the diagonal matrix of eigenvalues.
Show that if a matrix is orthogonal and its determinant is then each element of the matrix is equal to its own cofactor. Hint: Use (6.13) and the definition of an orthogonal matrix.
Let each of the following matrices represent an active transformation of vectors in (x,y)plane (axes fixed, vector rotated or reflected).As in Example 3, show that each matrix is orthogonal, find its determinant and find its rotation angle, or find the line of reflection.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
