- #1

soopo

- 225

- 0

**Is the following matrix isomorphic?**

## Homework Statement

a) Is the following matrix isomorphic?

[tex] L: \Re^{2} \rightarrow \Re^{2} [/tex]

[tex] L(x) = (-x_{2}, 0), where x = (x_{1}, x_{2}) \in \Re^{2}.[/tex]

b)

Define Ker(L) and Im(L).

## The Attempt at a Solution

a) I need to show that the L is bijection. I know that it is injection,

because it can be presented as Ax = b. The mapping is also linear, so L is

surjection. Thus, L is bijection and isomorphic.

b)

[tex]Ker(L) = \Re^{2}[/tex]

[tex]Im(L) = \Re^{2}[/tex]

I am not sure is this enough.

Last edited: