2. Linear mapsConsider the following three vectors in R³:~-0) -- () --OV1 ==V3 =1(a) Show that 6 = (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 R¹.A linear map T: Rª →] R³ is determined by:T(u₁)= V₁, T(u₂) = 2v₂,=T(u3) = T(u4) = 0,

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- Linear maps Consider the following three vectors in R³: 1 0 --0) --(9)· --0 V1 = 1 V3 = = -1 1 (a) Show that 6 = (V₁, V2, V3) is a basis for R³. Consider the following four vectors in Rª: 1 --0---0---0--0 = 1 = 1 1 = (b) Show that B = (U₁, U2, U3, U4) is a basis for Rª. = 1 1

- Linear maps Consider the following three vectors in R³: 1 0 --0) --(9)· --0 V1 = 1 V3 = = -1 1 (a) Show that 6 = (V₁, V2, V3) is a basis for R³. Consider the following four vectors in Rª: 1 --0---0---0--0 = 1 = 1 1 = (b) Show that B = (U₁, U2, U3, U4) is a basis for Rª. = 1 1

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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Question

2. Linear maps
Consider the following three vectors in R³:
~-0) -- () --O
V1 =
=
V3 =
1
(a) Show that 6 = (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 R¹.
A linear map T: Rª →] R³ is determined by:
T(u₁)= V₁, T(u₂) = 2v₂,
=
T(u3) = T(u4) = 0,

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