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? ? ? Are the following statements true or false? 1. For a square matrix A, vectors in the column space of A are orthogonal to vectors in the nullspace of A. + 2. For any scalar c and any vector v ER", ||cv|| = cl|v||. 3. If ||u||² + ||v||² = ||uv||², then the vectors u and v are orthogonal.

? ? ? Are the following statements true or false? 1. For a square matrix A, vectors in the column space of A are orthogonal to vectors in the nullspace of A. + 2. For any scalar c and any vector v ER", ||cv|| = cl|v||. 3. If ||u||² + ||v||² = ||uv||², then the vectors u and v are orthogonal.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 45E
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? ? ? ? ? Are the following statements true or false? 1. For a square matrix A, vectors in the column space of A are orthogonal to vectors in the nullspace of A. 2. For any scalar c and any vector v ER", ||cv|| = c||v||. 3. If ||u||² + ||v||² = ||u – v||², then the vectors u and v are orthogonal. - 4. If y = Z₁ + Z₂, where Z₁ is in a subspace W and Z₂ is in W, then Z₁ must be the orthogonal projection of y onto W. 5. If the distance between vectors u and v is equal to the distance between u and -v, then u and v are orthogonal.
Transcribed Image Text:? ? ? ? ? Are the following statements true or false? 1. For a square matrix A, vectors in the column space of A are orthogonal to vectors in the nullspace of A. 2. For any scalar c and any vector v ER", ||cv|| = c||v||. 3. If ||u||² + ||v||² = ||u – v||², then the vectors u and v are orthogonal. - 4. If y = Z₁ + Z₂, where Z₁ is in a subspace W and Z₂ is in W, then Z₁ must be the orthogonal projection of y onto W. 5. If the distance between vectors u and v is equal to the distance between u and -v, then u and v are orthogonal.
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