# help with linear maps

I came across this question whilst revising:

give the general expresion h(x,y,z) for the linear map h:$\mathbb{R}^3$ $\to$ $\mathbb{R}^3$ defined by h(1,1,1)=(2,2,0), h(1,2,1)=(3,3,0) and h(1,0,0)=(1,0,1)

in the answer it says:

(x,y,z)=(-y+2z)(1,1,1)+(y-z)(1,2,1)+(x-z)(1,0,0) then linearity implies h(x,y,z)=(x+y,y+z,x-z)

I dont understand how to arrive at the final answer. i found that (x+y,y+z,x-z) = (1,1,0),(0,1,1),(0,1,-1). is this a standard expression?

• Try to write with LaTeX, otherwise is between very hard and utterly impossible to understand. Also, what is that r*3 thingy there...?? – DonAntonio Dec 28 '13 at 17:22
• sorry \mathbb{R}^3 is r*3 – user107783 Dec 28 '13 at 17:25