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

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