Given the following system of linear equations: 3x, + 4x, 1 %3D 2x, 2x, + = -1. 2x, 2x, + 4x, = 0 %3D Describe v, A and b if the convention used is v. A =b. Determine the linear transformation Tthat A represents by the convention (v)T = v- A. Find the standard matrix A' of Tif the convention T(v)= A' v is used instead.

Given the following system of linear equations: 3x, + 4x, 1 %3D 2x, 2x, + = -1. 2x, 2x, + 4x, = 0 %3D Describe v, A and b if the convention used is v. A =b. Determine the linear transformation Tthat A represents by the convention (v)T = v- A. Find the standard matrix A' of Tif the convention T(v)= A' v is used instead.

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.
Given the following system of linear equations:
3x, + 4x,
2x,
2x, +
-1.
2x,
X2
2.x, + 4x,
(a) Describe v, A and b if the convention used is v. A = b.
(b) Determine the linear transformation T'that A represents by the convention (v)T = v. A.
(c) Find the standard matrix A' of Tif the convention T(v) = A' v is used instead.
(d) Suppose that the system is consistent, investigate whether (-5,5,0) e Im T.
+2y, + y,
(e) Suppose S:R →R' is a linear transformation defined by S y,
+5y,
Determine the standard matrix C for SoT using the convention SoT(v)% C v.

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