# Finding spanning sets

• Mar 27th 2013, 07:58 PM
mrmaaza123
Finding spanning sets
Let W = { [a+b a-b a+2b] , a,b are in R} its a 3*1 matrix, a+b , a-b and a+2b are actually the first elements of three different rows. Find any three spanning sets for W? I managed to find one,
a (1 1 1) + b(1 1 1) , both of these are also 3*1 matrices where each 1 is the first element of the first three rows.
How do i find the other two ?
Sorry about my notation.

• Mar 28th 2013, 05:25 PM
chiro
Re: Finding spanning sets
Hey mrmaaza123.

Hint: Try multiplying the vectors by some constant.
• Mar 28th 2013, 05:47 PM
HallsofIvy
Re: Finding spanning sets
Quote:

Originally Posted by mrmaaza123
Let W = { [a+b a-b a+2b] , a,b are in R} its a 3*1 matrix, a+b , a-b and a+2b are actually the first elements of three different rows. Find any three spanning sets for W? I managed to find one,
a (1 1 1) + b(1 1 1)

Do you not mean a[1, 1, 1]+ b[1, -1, 2]

Quote:

, both of these are also 3*1 matrices where each 1 is the first element of the first three rows.
How do i find the other two ?
Sorry about my notation.