PN220 Vectors and Vector Operations

I’ll provide a series of detailed questions on vectors and their operations in linear algebra. These range from basic to intermediate level, assuming vectors in $mathbb{R}^n$ (real n-dimensional space). Each question includes a clear statement, followed by a step-by-step solution or explanation. I’ve used standard notation: vectors are in bold (e.g., $mathbf{u}$), and operations are defined accordingly.

Requirements:

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