2. Vector NotationIn this course we will do a lot of calculations on vectors and matrices. This especially requiresextensive use of the transpose operator. For example, a 3x3 matrix can be denoted equally by their row orcolumn vectors:PiP2= ( r} r} r} )" = ( ef & d )A3×3 =P3A rigid transformation on homogenous coordinates in space can be described with the following matrix:r11r12r13t1- ( )-Rtr22 r23 t2t3r21A =r31r32r3310 01Make yourself familiar with the alternative notations. What is the simplest way to describe the product of thismatrix with a 4-vector v =(#1, 82, 23, w)" = (x", w)" ?

We have to find out the simplest way to describe the product of A and v. The matrix A is given, that…

Answered: Make yourself familiar with the…

Make yourself familiar with the alternative notations. What is the simplest way to describe the product of this matrix with a 4-vector v = (x1,x2, x3, w)T = (x", w)" ?

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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Question

2. Vector Notation
In this course we will do a lot of calculations on vectors and matrices. This especially requires
extensive use of the transpose operator. For example, a 3x3 matrix can be denoted equally by their row or
column vectors:
Pi
P2
= ( r} r} r} )" = ( ef & d )
A3×3 =
P3
A rigid transformation on homogenous coordinates in space can be described with the following matrix:
r11
r12
r13
t1
- ( )-
R
t
r22 r23 t2
t3
r21
A =
r31
r32
r33
1
0 0
1
Make yourself familiar with the alternative notations. What is the simplest way to describe the product of this
matrix with a 4-vector v =
(#1, 82, 23, w)" = (x", w)" ?

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