Week 1 (lec 1-3) Lecture Notes

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Rather than view as the set of all points with real coordinates. (ie. we will view as a set of vectors. Vectors will be written mainly as column matrices. The origin is also known as the zero vector. You can perform operations in with vectors that you can"t do with points. Let . and be two vectors in . If for then is a linear combination of . Math 136 page 1 is a combination of. There are 10 important properties that hold for vectors in. For each , there exists vector where . Also, note that by properties 1 & 6, is closed under linear combinations. This means that any linear combination of vectors in is still a vector in . This is an important property we will want when taking groups of vectors from . Let be the set of all scalar multiples of (the vector equation of )

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