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1. Justify your answers below. (a) True or False : The function T :R → R defined by T(r) = x² is a linear map. False : If B = {() . (1)} and B' = -{()- ()}- (b) True or are basis for R² and T:R? → R² is any linear map, then T# ("() "()) (c) Let T : R$ → R° and T(F) = Ai where A is the standard matrix. Supposing A is invertible, compute the rank of T. %3D

1. Justify your answers below. (a) True or False : The function T :R → R defined by T(r) = x² is a linear map. False : If B = {() . (1)} and B' = -{()- ()}- (b) True or are basis for R² and T:R? → R² is any linear map, then T# ("() "()) (c) Let T : R$ → R° and T(F) = Ai where A is the standard matrix. Supposing A is invertible, compute the rank of T. %3D

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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1. Justify your answers below. (a) True or False : The function T :R → R defined by T(r) = x² is a linear map. False : If B = {() . (1)} and B' = -{()- ()}- (b) True or are basis for R² and T:R? → R² is any linear map, then T# ("() "()) (c) Let T : R$ → R° and T(F) = Ai where A is the standard matrix. Supposing A is invertible, compute the rank of T. %3D
Transcribed Image Text:1. Justify your answers below. (a) True or False : The function T :R → R defined by T(r) = x² is a linear map. False : If B = {() . (1)} and B' = -{()- ()}- (b) True or are basis for R² and T:R? → R² is any linear map, then T# ("() "()) (c) Let T : R$ → R° and T(F) = Ai where A is the standard matrix. Supposing A is invertible, compute the rank of T. %3D
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