Let

V={(x ,x ,x ,x ,x ) R : x -2x +3x -x +2x =0}.

(a) Show that S={(0,1,1,1,0)} is a linearly independent subset of V.

(b) Extend S to a basis for V.

- Oct 26th 2010, 07:05 PMtn11631Show that S in linearly Independent and how to extend S to a basis for V
Let

V={(x ,x ,x ,x ,x ) R : x -2x +3x -x +2x =0}.

(a) Show that S={(0,1,1,1,0)} is a linearly independent subset of V.

(b) Extend S to a basis for V. - Oct 27th 2010, 06:41 AMHallsofIvy
A set containing a single non-zero vector is

**always**a linearly independent subset! If av= 0 and v is not 0 then you must have a= 0. Do you see how that verifies the**definition**of "linearly independent"? Here, all you need to do is show that (0, 1, 1, 1, 0) is in V. becomes 0- 2(1)+ 3(1)- 1+ 2(0)= 0. Is that true?

Quote:

(b) Extend S to a basis for V.