Show that every vector in T1 = span {(1,0,0); (0,1,0); (0,0,1)} are in also in T2 Та %3 span {(1,1,0); (0,0,1); (1,0,1)}, i.e. show explicitly how , in T2 corresponds to some given t, in T1.
Show that every vector in T1 = span {(1,0,0); (0,1,0); (0,0,1)} are in also in T2 Та %3 span {(1,1,0); (0,0,1); (1,0,1)}, i.e. show explicitly how , in T2 corresponds to some given t, in T1.
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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Question
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![6. Show that every vector in \( T_1 = \text{span} \{ (1,0,0); (0,1,0); (0,0,1) \} \) are also in
\[ T_2 = \text{span} \{ (1,1,0); (0,0,1); (1,0,1) \}, \]
i.e., show explicitly how \( \vec{t}_2 \) in \( T_2 \) corresponds to some given \( \vec{t}_1 \) in \( T_1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20fbb71c-9fd5-4b59-9900-a3864652c523%2Fb5e5b6d1-a6e0-4c78-9259-19ffad307db8%2Fyabtcwk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Show that every vector in \( T_1 = \text{span} \{ (1,0,0); (0,1,0); (0,0,1) \} \) are also in
\[ T_2 = \text{span} \{ (1,1,0); (0,0,1); (1,0,1) \}, \]
i.e., show explicitly how \( \vec{t}_2 \) in \( T_2 \) corresponds to some given \( \vec{t}_1 \) in \( T_1 \).
Expert Solution
Step 1
Consider the vector space and
Let be an arbitrary vector. Therefore it can be represented as:
Let be an arbitrary vector. Therefore it can be represented as:
Solving them for , we have:
Therefore and
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