Answered: The following matrices are given:…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The following matrices are given: Matrix A describes the reflection of a point in space on the x, y -plane and matrix B represents the rotation of the spatial coordinate system around the z-axis by the angle alpha (a) Show that both matrices are orthogonal. (b) Find the inverse of the two matrices. (c) Write the following matrices: (i) A matrix that describes the reflection of a point in space on the x, z-plane, (ii) A matrix that describes the rotation of the spatial coordinate system around the y-axis by the angle ß

1 0
COS a
sin a
A =
1
und B =
- sin a
COs a
0 0
-1
0 1

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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