Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Precalculus Mathematics Homework Help
How to check if a transformation is surjective and injective
Reply to thread
Message
[QUOTE="mathwonk, post: 5909123, member: 13785"] These concepts can be tricky to describe. Technically I feel it is important to begin the statement with the element y in the target space, so that the quantifiers are in the right order. One way I like is to say that f is injective if for every y in the target space, there is at most one x in the domain, or source space, such that f(x) = y. Then one can say analogously that f is surjective if for every y in the target space, there is at least one x in the source space such that f(x) = y. then the OP might check that in case every row has a pivot, that no matter what column vector y he puts on the right, he will be able to find an x such that T(x) = y. Thus T is surjective. And if every column has a pivot, no matter what column y he puts on the right, he will not be able to find more than one x with T(x) = y. In this last case, injectivity, it will be sufficient to show that if he puts the zero column y on the right, then the only solution is the zero vector x. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Precalculus Mathematics Homework Help
How to check if a transformation is surjective and injective
Back
Top