3. Let L: R4 R₂ be the linear transformation defined by L ([u₁ U2 U3 U4] u₁]) = [u₁ + U3 u₂+ U₁] (a) Is [23 - 2 3] in ker L? (d) Is [00] in range L? (b) Is [4 (e) Find ker L. (c) Is [1 2] in range L? (f) Find a set of vectors spanning range L. - 24 4 2] in ker L?
3. Let L: R4 R₂ be the linear transformation defined by L ([u₁ U2 U3 U4] u₁]) = [u₁ + U3 u₂+ U₁] (a) Is [23 - 2 3] in ker L? (d) Is [00] in range L? (b) Is [4 (e) Find ker L. (c) Is [1 2] in range L? (f) Find a set of vectors spanning range L. - 24 4 2] in ker L?
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...
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![3. Let L: R4 → R₂ be the linear transformation defined by
L ([u1 12 13
= [U₁ + U3
u4])
U4])
U2
(a) Is [23 - 2 3] in ker L?
(b) Is [4 2 - 4 2] in ker L?
(c) Is [1 2] in range L?
+u4]
(d) Is [00] in range L?
(e) Find ker L.
(f) Find a set of vectors spanning
range L.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0cfa59ce-5074-4e94-af68-42c59c01b835%2F29790d65-2d36-4e60-8cab-958a303b4618%2Fcrkj95i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let L: R4 → R₂ be the linear transformation defined by
L ([u1 12 13
= [U₁ + U3
u4])
U4])
U2
(a) Is [23 - 2 3] in ker L?
(b) Is [4 2 - 4 2] in ker L?
(c) Is [1 2] in range L?
+u4]
(d) Is [00] in range L?
(e) Find ker L.
(f) Find a set of vectors spanning
range L.
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