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*1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x² + x² + x³ =1} (f) (x = R³: x² + x² + x² = −1} ---0-0-0 (h) (x = R¹ : x= for some s, t = R}

*1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x² + x² + x³ =1} (f) (x = R³: x² + x² + x² = −1} ---0-0-0 (h) (x = R¹ : x= for some s, t = R}

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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*2. For each pair of vectors in Exercise 1, calculate proj,x and proj,y. *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x² = 1) (f) (x = R³: x + x + x = -1} -0-0-0₁ +s + (h) (x = R¹ : x= for some s, 1 = R}
Transcribed Image Text:*2. For each pair of vectors in Exercise 1, calculate proj,x and proj,y. *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x² = 1) (f) (x = R³: x + x + x = -1} -0-0-0₁ +s + (h) (x = R¹ : x= for some s, 1 = R}
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