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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 30E
Related questions
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6397ed9c-afe2-4dd0-b1f7-1b23fa036739%2F58aca158-35db-4760-853f-c8c4da43565d%2F6td8dec_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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