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Consider the following subspaces of R4: and U₁ = {(a, b, b, c): a, b, c ER} := U₂ = {(a, b, 0, a): a, b = R}. (a) For i 1,2, find a matrix A, such that U; is the solution set of the homogeneous equation A₁70 for 7 € R¹. (b) By first stacking your matrices A₁ and A₂ on top of each other and then applying row reduction, compute the subspace formed from the intersection Uլ Ո Ս.

Consider the following subspaces of R4: and U₁ = {(a, b, b, c): a, b, c ER} := U₂ = {(a, b, 0, a): a, b = R}. (a) For i 1,2, find a matrix A, such that U; is the solution set of the homogeneous equation A₁70 for 7 € R¹. (b) By first stacking your matrices A₁ and A₂ on top of each other and then applying row reduction, compute the subspace formed from the intersection Uլ Ո Ս.

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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Consider the following subspaces of R¹: and U₁ := {(a, b, b, c): a, b, c ≤ R} U₂ := {(a, b, 0, a) : a,b ≤ R}. (a) For i = 1,2, find a matrix Aį such that U; is the solution set of the homogeneous equation A=0 for 7 € R¹. (b) By first stacking your matrices A₁ and ₂ on top of each other and then applying row reduction, compute the subspace formed from the intersection Uլ Ո՛Ս.
Transcribed Image Text:Consider the following subspaces of R¹: and U₁ := {(a, b, b, c): a, b, c ≤ R} U₂ := {(a, b, 0, a) : a,b ≤ R}. (a) For i = 1,2, find a matrix Aį such that U; is the solution set of the homogeneous equation A=0 for 7 € R¹. (b) By first stacking your matrices A₁ and ₂ on top of each other and then applying row reduction, compute the subspace formed from the intersection Uլ Ո՛Ս.
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