CS223 · Annotated SlidesChapter 1 — Linear Independence
Chapter 1 · Annotated slides

Linear Independence

Linear independence and dependence of vectors and of a matrix’s columns, special cases (one vector, two vectors, more vectors than entries, the zero vector).

Slide text Study notes Highlight: key words Tips, tricks & traps Seen again elsewhere How it can come up
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      Slide 4: Linearly Linearly independent A Set of One dependent
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        1. Facts: a set containing 0 is dependent; two vectors are dependent ⇔ one is a multiple of the other; MORE vectors than entries (p > n) ⇒ dependent.
        Memory trickp vectors in ℝⁿ with p > n are always dependent.
        🎯 How this can come up · 2 questions
        MCQ

        Four vectors in ℝ³ are:

        True / False

        If a set contains the zero vector, it is linearly dependent.

        Example:

        Is this set of vectors linearly independent

        Yes, the vectors u and v are linearly independent because neither vector is a multiple of the other

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          Example:

          Is this set of vectors linearly independent

          No, the vectors are linearIy dependent because there are three vectors in the set and there are only two entries in each vector Notice, even though none of the vectors is a multiple of one of the other vectors

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