# MATH136 Quiz: theorems

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Note: theorem numbering typically occurs in order, however, there are a few times when a number gets skipped. There are no theorems missing from this le. If (cid:126)x, (cid:126)y, (cid:126)w rn and c, d r, then. V2 ((cid:126)x + (cid:126)y) + (cid:126)w = (cid:126)x + ((cid:126)y + (cid:126)w) V3 (cid:126)x + (cid:126)y = (cid:126)y + (cid:126)x. V4 there exists a vector (cid:126)0 rn, called the zero vector, such that (cid:126)x + (cid:126)0 = (cid:126)x. V5 there exists a vector (cid:126)x rn such that (cid:126)x + ( (cid:126)x) = (cid:126)0. V8 (c + d)(cid:126)x = c(cid:126)x + d(cid:126)x. V9 c((cid:126)x + (cid:126)y) = c(cid:126)x + c(cid:126)y. If (cid:126)vk can be written as a linear combination of (cid:126)v1, . , (cid:126)vk} in rn is linearly dependent if and only if (cid:126)vi span{(cid:126)v1, . , (cid:126)vk} for some i, 1 i k. , (cid:126)vk} contains the zero vector then it is linearly dependent. Let s be a non-empty subset of rn.