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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)
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.
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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