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Consider the linear map T : Rª →→→ R¹, x→→→→ Ax, where [0 2 0 1 2 1 For which a is T one-to-one? A 0-2 a 5 2-4 1 0

Consider the linear map T : Rª →→→ R¹, x→→→→ Ax, where [0 2 0 1 2 1 For which a is T one-to-one? A 0-2 a 5 2-4 1 0

Advanced Engineering Mathematics
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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Need help with this matrix algebra qusetion.

Consider the linear map T : R4 →→→→ R¹, x→→→→→ Ax, where 0 2 0 1 2 1 -1 0-2 a 5 2-4 1 0 For which a is T one-to-one? A
Transcribed Image Text:Consider the linear map T : R4 →→→→ R¹, x→→→→→ Ax, where 0 2 0 1 2 1 -1 0-2 a 5 2-4 1 0 For which a is T one-to-one? A
Expert Solution
Step 1: Given the information

The given matrix,

A equals open square brackets table row 0 2 0 cell negative 1 end cell row 1 2 1 cell negative 1 end cell row 0 cell negative 2 end cell a 5 row 2 cell negative 4 end cell 1 0 end table close square brackets

The aim is to find the values of a for which the linear map T is one-to-one.

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