Hey, i've done this problem but i don't know what it all means? What does it mean to form a basis?(adsbygoogle = window.adsbygoogle || []).push({});

Problem: show that the vectors (1,1) , (1, -1) form a basis for R^2

(x,y) = a1(1, 1) + b1(1, -1)

x = a1 + b1 => a1 = x - b1

y= a1- b1 => b1 = a1-y

a1 = x - a1 + y

2a1 = x + y

a1 = 1/2(x + y) <----- What does this represent?

b1 = (x-b1)-y

2b1 = x - y

b1 = 1/2(x-y) <----- What does this represent?

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# Homework Help: Bases and Vectors

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