I am having problems in my linear algebra class. The class is taught rather poorly. There is only but 3 students left. The instructor is of no help. I tried reading my txtbook and following a few videos (even went to office hours). However I am not understanding Isomorphism.(adsbygoogle = window.adsbygoogle || []).push({});

I know that a transformation from V to W is a linear transformation from a vector space V to a vector space W, when V maps district vectors into W. (Thinking of a function that is 1 to 1)

@and onto if every vector in W is the image of at least one vector in V.

I am using Anton Elementary Linear algebra txt.

From my understanding. The first property is to prove 1 to 1. The second is to prove onto?

There is an example in my book. P 466.

Let V= R^inffinty. Be the sequence space in which u1, u2,..., un,... is an infinite sequence of Real numbers..

Consider the linear "sshifting operators" on V defined by

T1 (u1, u2,..., un,...)=(0, u1, u2,...un,... )

T2 (u1, u2,..., un,...)=(u2, u3,...un,...)

(a) Show that T1 is one to one but not not onto.

what am I supposed to do? I am lost.

Maybe?

Let a=a1,a2,..., an,... and b=b1, b2,..., bn,... be a sequence of infinite real numbers in V.

T1 (a+b)=(0, a1+b1, a2+b2,...an+bn,...)

T1 (a)+T(b)=(0, a1, a2,...an,...)+(0, b1, b2,...bn,...)

Which equals the previous line? How would I show that it fails for multp. By scalar? Thanks

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# Not Understanding Isomorphism. Please help.

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