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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.

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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? ? ? ? ? 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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