How Do Eigenvectors Relate to Matrix Dimensions and Images?

[jwqwerty]

Homework Statement

1. If v is any nonzero vector in R^2, what is the dimension of the space V of all 2x2 matrices for which v is an eigenvector?

2. If v is an eigenvector of matrix A with associated eigenvalue 3, show that v is in the image of matrix A

Homework Equations

If v is an eigenvector with eigenvalue c(real number), then Av=cv (definition of eigenvector)

The Attempt at a Solution

i have posted a picture for my attempt at the first question
but i totally have no idea on the second question
need help from you guys!

 

[jwqwerty]

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