The second column of the matrix of change of basis from the basis B = {u= (1,1,1); v = (1,0,1); w = (0,1,1) } to the basis B'= {r= (3,4,1); s = (3,0,1); = (1,2,0) } isO A3OB 402O D.0O E.11-101

Answered: The second column of the matrix of…

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

The second column of the matrix of change of basis from the basis B = {u= (1,1,1); v = (1,0,1); w = (0,1,1) } to the basis B'= {r= (3,4,1); s = (3,0,1); = (1,2,0) } is
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OB 4
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1
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1

Expert Solution

Step 1

What is Change of Basis:

Any element of a vector space of finite dimension n can be uniquely represented in mathematics by a vector of coordinates, which is a sequence of n scalars referred to as coordinates. The coordinate vector that represents a vector v on one basis differs generally from the coordinate vector that represents v on the other basis when two separate bases are taken into account. Every assertion that is expressed in terms of coordinates related to one basis must be changed into an assertion that is expressed in terms of coordinates relative to the other basis.

To Determine:

We determine the second column of the change of basis matrix from the basis $\begin{array}{rcl} B & = & \{u = (1, 1, 1), v = (1, 0, 1), w = (0, 1, 1)\} \end{array}$ to the basis $\begin{array}{rcl} B' & = & \{r = (3, 4, 1), s = (3, 0, 1), t = (1, 2, 0)\} \end{array}$ .