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8. Suppose that S = {ü1, v2, v3} is a set of linearly independent vectors in R4. Answer the following true or false questions by circling ONLY ONE of TRUE or FALSE. Make sure to include your reasoning. (a) Any vector u in R' can be written as a linear combination of u1, 02, 03. TRUE FALSE (b) The vector ü3 can be written as a linear combination of ij and 02. TRUE FALSE (c) There is a vector 74 such that {ũ1, 02, 03, 04} is a basis for R4. TRUE FALSE

8. Suppose that S = {ü1, v2, v3} is a set of linearly independent vectors in R4. Answer the following true or false questions by circling ONLY ONE of TRUE or FALSE. Make sure to include your reasoning. (a) Any vector u in R' can be written as a linear combination of u1, 02, 03. TRUE FALSE (b) The vector ü3 can be written as a linear combination of ij and 02. TRUE FALSE (c) There is a vector 74 such that {ũ1, 02, 03, 04} is a basis for R4. TRUE FALSE

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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please send handwritten solution for Q 8 part c
8. Suppose that S = {õ1, 02, v3} is a set of linearly independent vectors in R4. Answer the following true or false questions by circling ONLY ONE of TRUE or FALSE. Make sure to include your reasoning. (a) Any vector w in Rª can be written as a linear combination of T1, v2, 03. TRUE FALSE (b) The vector ū3 can be written as a linear combination of ij and ö2. TRUE FALSE (c) There is a vector v4 such that {ũ1, 02, 03, 74} is a basis for R4. TRUE FALSE
Transcribed Image Text:8. Suppose that S = {õ1, 02, v3} is a set of linearly independent vectors in R4. Answer the following true or false questions by circling ONLY ONE of TRUE or FALSE. Make sure to include your reasoning. (a) Any vector w in Rª can be written as a linear combination of T1, v2, 03. TRUE FALSE (b) The vector ū3 can be written as a linear combination of ij and ö2. TRUE FALSE (c) There is a vector v4 such that {ũ1, 02, 03, 74} is a basis for R4. TRUE FALSE
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