Let U₁, U2, U3 – be the following subspaces of Rª U₁={a, b, c, d)=R4| ²b=c; a=d=0}; U2={(a, b, c, d)=R4| a - b + 3¹c + 4;d=0, -a +b - 3¹c - 4 d=0}; U3= {a, b, c, d)=R4| 2a − 3b − 2 c - d=0, a + 2b + 0c + .² d=0 }; and the dimension () of U₁. Sub-Task 1. Find a basis Sub-Task 2. Find a basis () and the dimension () of U₂. Sub-Task 3. Find a basis (^.¯ _ `) and the dimension (´¸ ¯`) of U3. Sub-Task 4. Whether Rª=U₁+U2, (provide a justification). (. ). Whether R¹=U₁U2, (provide a justification). (~ 1 Sub-Task 5. Whether Rª=U₁+U3, (provide a justification) ^ Whether Rª=U₁ÐU3, (provide a justification). (^´ ^^). Sub-Task 6. Whether Rª=U2+U3, (provide a justification). (u. (provide a justification). (¯¸). *). Whether R4=U₂ÐU3,
Let U₁, U2, U3 – be the following subspaces of Rª U₁={a, b, c, d)=R4| ²b=c; a=d=0}; U2={(a, b, c, d)=R4| a - b + 3¹c + 4;d=0, -a +b - 3¹c - 4 d=0}; U3= {a, b, c, d)=R4| 2a − 3b − 2 c - d=0, a + 2b + 0c + .² d=0 }; and the dimension () of U₁. Sub-Task 1. Find a basis Sub-Task 2. Find a basis () and the dimension () of U₂. Sub-Task 3. Find a basis (^.¯ _ `) and the dimension (´¸ ¯`) of U3. Sub-Task 4. Whether Rª=U₁+U2, (provide a justification). (. ). Whether R¹=U₁U2, (provide a justification). (~ 1 Sub-Task 5. Whether Rª=U₁+U3, (provide a justification) ^ Whether Rª=U₁ÐU3, (provide a justification). (^´ ^^). Sub-Task 6. Whether Rª=U2+U3, (provide a justification). (u. (provide a justification). (¯¸). *). Whether R4=U₂ÐU3,
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 4CM: Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4,...
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