subspace? zero vector? (0,0,0) aU still of form s(0,1,0) + t(0,0,1) x,y

208 day 9 February 24, 2015
subspace?
zero vector? (0,0,0)
aU still of form s(0,1,0) + t(0,0,1)
x,y in U x+y in U
(0,s,t) + (0, a, b) = (0, a+s, b+t)
208 day 9 February 24, 2015
(0,x+1,x) + (0,y+1,y) = (0, x+y+2, X+y) not a subspace
208 day 9 February 24, 2015
208 day 9 February 24, 2015
208 day 9 February 24, 2015
208 day 9 February 24, 2015
208 day 9 February 24, 2015
208 day 9 February 24, 2015
linearly independant
{x1,x2,...,xn}
a1x1+a2x2+....anxn=0
a1=a2=...=an=0
ex: [0 1] [1 0]
a[0 1] + b [ 1 0] = [ 0 0]
[ 0 a ] + [ b 0] = [b a ] = [ 0 0]
these are linearly independant
208 day 9 February 24, 2015
[ 1 0 ] [2 3] [ 4 2]
a[ 1 0 ]+b[2 3]+ c[ 4 2]= [0 0]
a + 2b + 4c = 0
3b + 2c = 0
b = ­2 c = 3 a = ­8 NOT linearly independant