show that 100 010 001 span R3 if v1v2vp are vectors in Rndef

show that [1,0,0], [010] ,[001] span R³

if v₁,v_2,.......v_p are vectors in Rⁿ,define span {v_1,v_2,...Vp}.

use a geometric approach to show that [1,0], [01] span R^2.

Solution

1.

Any vector in R3 is

[x,y,z] where x,y,z are any real numbers

[x,y,z]=x[1,0,0]+y[0,1,0]+z[0,0,1]

Hence, given three vectors span R3

2.

Span {v1,v2,...,vp} is set of all linear combinations of v1,....vp

3. [1 0] is the unit vector along x axis

[0 1] is unit vector along y axis

Any vector in R2 can be uniquely written as component along x and y axis

Hence given two vectors span R2