18.06 Lecture Notes - Lecture 1: The World Academy Of Sciences, Grater, Block Matrix
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Such as c = 2 and d = 1 that produces cv + dw = (4, 5) Other times we want all the combinations of v and w. When w is not on that line, the combinations cv + dw ll the whole two-dimensional plane. Column vector: v = where v1 is the rst component and v2 is the second component. Vector addition: v = and w = add to v + w = Combining addition with scalar multiplication, we now form linear combinations of v and w. Multiply v by c and multiply w by d; then add cv + dw. De nition: the sum of cv and dw is a linear combination of v and w. The zero vector is always a possible combination. Every time we have a space of vectors, that zero vector will be included cv + 0w = vector cv in the direction of v.
