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Roo2
#4
Oct31-10, 10:38 AM
P: 41
A couple linear algebra questions (basis and linear transformation

Quote Quote by lkh1986 View Post
For question 1 with the condition x + y + 2z = 0, try to express one of the variables in other two variables. For example, x = -y - 2z. Then, replace x with -y - 2z in {(x,y,z)|x,y,z are real}. Lastly, try to "factor" or decompose the vector into several vectors to get the basis.
Alright, I'll give it a shot.


x = -y -2z

{(y,z) | -y-2z, y, z}

{(y,z) | y(-1, 1, 0) + z(-2, 0, 1)}

Basis: {(-1, 1, 0), (-2, 0, 1)}

Is that correct?