MATH 240 Lecture Notes - Lecture 13: Gaussian Elimination, Row Echelon Form, Augmented Matrix
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1. 2 additional exercise: row reduce the following agumented matrix to reduced row. Show your working by showing the row operations you use. Note, there is more than one way to do this. You must end up with the same nal answer but your row operations may be very di erent than mine. Show that (u + v) + w) = u + (v + w) for vectors u, v, w rn. (u + v) + w = ([u1, . , un + (vn + wn)] by de nition of vector + Show that c(du) = (cd)u for u rn and scalars c, d r. c(du) = c(d[u1, . = c[du1, . dun] by de nition of for vectors by de nition of for vectors. = [(cd)u1, . (cd)un] because + in r is associative. = (cd)[u1, . un] by de nition of for vectors. 1. 5 additional exercise: describe all solutions of ax = 0 in parametric vector form for.