MAT 343 - Zandieh - Day 2\ The definition of the span of a set of vectors:\ DEFINITION\ If

v_(1),dots,v_(p)

are in

R^(n)

, then the set of all linear combinations of

v_(1),dots,v_(p)

\ is denoted by

Span{v_(1),dots,v_(p)}

and is called the subset of

R^(n)

spanned (or\ generated) by

v_(1),dots,v_(p)

. That is, Span

{v_(1),dots,v_(p)}

is the collection of all\ vectors that can be written in the form\

c_(1)v_(1)+c_(2)v_(2)+cdots+c_(p)v_(p)

\ with

c_(1),dots,c_(p)

scalars.\ Determine or describe each of the following:\ (a)

Span{[[3],[1]]}

\ (b)

Span{[[2],[3]],[[4],[6]]}

\ (c)

Span{[[1],[3]],[[4],[5]]}

\ (d)

Span{[[1],[3]],[[2],[-6]],[[4],[5]]}

\ (e)

Span{[[0],[0]],[[2],[3]]}

\ (f) Span

{[[1],[3],[2]],[[1],[4],[5]]}

\ (g)

Span{[[-3],[0],[-2]]}

\ In other words, tell whether each is a point, line, plane or other shape. Also, describe-\ using an equation, graph or other means - which point, line plane or other shape it is.

DEFINITION If v1,,vp are in Rn, then the set of all linear combinations of v1,,vp is denoted by Span{v1,,vp} and is called the subset of Rn spanned (or generated) by v1,,vp. That is, Span{v1,,vp} is the collection of all vectors that can be written in the form c1v1+c2v2++cpvp with c1,,cp scalars. Determine or describe each of the following: (a) Span{[31]} (b) Span{[23],[46]} (c) Span{[13],[45]} (d) Span{[13],[26],[45]} (e) Span{[00],[23]} (f) Span132,145 (g) Span302 In other words, tell whether each is a point, line, plane or other shape. Also, describe using an equation, graph or other means - which point, line plane or other shape it is