(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine whether each of the following mappings f is onto or one-to-one. Is f an isomorphism?

1) f maps R2 to R3 defined by f(x, y) = (x, y, x+y)

2) f maps R3 to R(1x3) defined by f(x,y,z) = [x^2, y^2, z^2]

3) f maps R4 to P2(R) defined by f(a,b,c,d) = a+(b-c)x+dx^2

2. Relevant equations

3. The attempt at a solution

I'm not sure how to do these.. I understand somewhat about one-to-one and onto, but these notations kind of confuse me.. For onto, do I just need to look at the outcome and see if it spans the space? And for one-to-one, I look at rather every component from the source appears in every component in the result?

1) Not one-to-one, onto.

2) Not one to one, onto.

3) Not one to one, onto.

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# Homework Help: Linear Algebra - one to one and onto question

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