If the matrix of change of basis form the basis B to the basis B' is A =(³)O A.OB.04 (3)00 (12)5221then the first column of the matrix of change of basis from B to B is:

Answered: If the matrix of change of basis form…

If the matrix of change of basis form the basis B to the basis B' is A = 21 OA. (²) 08 (1) OC (2) (¹) OD./ then the first column of the matrix of change of basis from B to B is:

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

If the matrix of change of basis form the basis B to the basis B' is A =
(³)
O A.
OB.
04 (3)
00 (12)
52
21
then the first column of the matrix of change of basis from B to B is:

Expert Solution

Step 1

Given information

The matrix of change of basis form the basis B to the basis B' is

$A = (\begin{matrix} 5 & 2 \\ 2 & 1 \end{matrix})$

Determinant of matrix A:-

$A = (\begin{matrix} 5 & 2 \\ 2 & 1 \end{matrix}) |A| = 5 (1) - 2 (2) |A| = 5 - 4 = 1 |A| = 1$

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