2. Given the following system of linear equations: 3x₂ + 4x₂ = 1 X₂ = -1. 2x, + 4x₂ = 0 2x₁ 2x₁ 2x₂ + (a) Describe v, 4 and b if the convention used is v. A = b. (b) Determine the linear transformation 7that A represents by the convention (v)T=v-A. (c) Find the standard matrix 4' of Tif the convention T(v)= A'-v is used instead. (d) Suppose that the system is consistent, investigate whether (-5,5,0) € Im 7. AL 3₁ [₁ +2₂+₁] 3₁ +5y₂ Determine the standard matrix C for SoT using the convention S-T(v)=C-v. (e) Suppose S: R' → R is a linear transformation defined by Sy
2. Given the following system of linear equations: 3x₂ + 4x₂ = 1 X₂ = -1. 2x, + 4x₂ = 0 2x₁ 2x₁ 2x₂ + (a) Describe v, 4 and b if the convention used is v. A = b. (b) Determine the linear transformation 7that A represents by the convention (v)T=v-A. (c) Find the standard matrix 4' of Tif the convention T(v)= A'-v is used instead. (d) Suppose that the system is consistent, investigate whether (-5,5,0) € Im 7. AL 3₁ [₁ +2₂+₁] 3₁ +5y₂ Determine the standard matrix C for SoT using the convention S-T(v)=C-v. (e) Suppose S: R' → R is a linear transformation defined by Sy
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![2.
Given the following system of linear equations:
3x, + 4x,
2.x, - 2x, +
x,
= -1.
2x,
2x, + 4x, = 0
(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 4' 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,]
y, +5y,
(e) Suppose S:R'R' is a linear transformation defined by S y,
Determine the standard matrix C for SoT using the convention S T(v) = C-v.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfe11947-ed05-4061-9fa2-a7f116314aff%2F8b2792e0-1b63-47b2-b5c9-41d593856818%2F9ouhpp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.
Given the following system of linear equations:
3x, + 4x,
2.x, - 2x, +
x,
= -1.
2x,
2x, + 4x, = 0
(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 4' 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,]
y, +5y,
(e) Suppose S:R'R' is a linear transformation defined by S y,
Determine the standard matrix C for SoT using the convention S T(v) = C-v.
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