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A linear map T : Rª → R³ is determined by: T(u₁)=v₁, T(u₂)=2v₂, T(U3)= T(u4) = 0, (c) Give the standard matrix of T, i.e., in terms of the standard bases for Rª and R³. (d) Give a basis for the image of T. (e) Give a basis for the kernel of T.

A linear map T : Rª → R³ is determined by: T(u₁)=v₁, T(u₂)=2v₂, T(U3)= T(u4) = 0, (c) Give the standard matrix of T, i.e., in terms of the standard bases for Rª and R³. (d) Give a basis for the image of T. (e) Give a basis for the kernel of T.

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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Just need help with C, D, E please

2. Linear maps Consider the following three vectors in R³: --0) --(-1) -- 0) = V2 = V3 (a) Show that C = = (V₁, V2, V3) is a basis for R³. Consider the following four vectors in Rª: --0---0--0--0 = 1 = (b) Show that B = (U1, U2, U3, U4) is a basis for Rª. A linear map T:R¹ → > R³ is determined by: (d) Give a basis for the image of T. = T(u₁)= V₁, T(u₂) = 2v₂, T(U3) = T(U4) = 0, (c) Give the standard matrix of T, i.e., in terms of the standard bases for R4 and R³. (e) Give a basis for the kernel of T. 1
Transcribed Image Text:2. Linear maps Consider the following three vectors in R³: --0) --(-1) -- 0) = V2 = V3 (a) Show that C = = (V₁, V2, V3) is a basis for R³. Consider the following four vectors in Rª: --0---0--0--0 = 1 = (b) Show that B = (U1, U2, U3, U4) is a basis for Rª. A linear map T:R¹ → > R³ is determined by: (d) Give a basis for the image of T. = T(u₁)= V₁, T(u₂) = 2v₂, T(U3) = T(U4) = 0, (c) Give the standard matrix of T, i.e., in terms of the standard bases for R4 and R³. (e) Give a basis for the kernel of T. 1
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