0 like 0 dislike
214 views
Let $\mathcal{S}$ be the linear space of infinite sequences of real numbers $x:=\left(x_{1}, x_{2}, \ldots\right) .$ Define the linear map $L: \mathcal{S} \rightarrow \mathcal{S}$ by
$L x:=\left(x_{1}+x_{2}, x_{2}+x_{3}, x_{3}+x_{4}, \ldots\right) .$
a) Find a basis for the nullspace of $L$. What is its dimension?
b) What is the image of $L ?$ Justify your assertion.
c) Compute the eigenvalues of $L$ and an eigenvector corresponding to each eigenvalue.
| 214 views

0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike