✓? ? ? ? True False Are the following statements true or false? 1. For all vectors u, v E R", we have u v = -v.u. 2. For any vector v ER", we have v . v = ||v|| . 3. If the distance between vectors u and v is equal to the distance between u and -v, then u and v are orthogonal. 4. For any scalar c and any vector v ER", ||cv|| = c||v|| . 5. For a square matrix A, vectors in the column space of A are orthogonal to vectors in the nullspace of A.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 48E
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Hi.I got the answer to this question wrong even after asking an expert so please can you give it another go and help me with the solutions to this problem. Thank you

✓?
?
?
?
True
False
Are the following statements true or false?
1. For all vectors u, v E R", we have u v = -v.u.
2. For any vector v ER", we have v . v = ||v|| .
3. If the distance between vectors u and v is equal to the distance between u and -v, then u and v are orthogonal.
4. For any scalar c and any vector v € R", ||cv|| = c||v|| .
5. For a square matrix A, vectors in the column space of A are orthogonal to vectors in the nullspace of A.
Transcribed Image Text:✓? ? ? ? True False Are the following statements true or false? 1. For all vectors u, v E R", we have u v = -v.u. 2. For any vector v ER", we have v . v = ||v|| . 3. If the distance between vectors u and v is equal to the distance between u and -v, then u and v are orthogonal. 4. For any scalar c and any vector v € R", ||cv|| = c||v|| . 5. For a square matrix A, vectors in the column space of A are orthogonal to vectors in the nullspace of A.
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