- 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
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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![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,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54b4ce07-0f16-474a-a4ca-6c3455490c69%2F21c3121e-0fef-48af-a904-bd8f445451bb%2F0jv81d_processed.png&w=3840&q=75)
Transcribed Image Text: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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