2×2 matrix with one single eigenvalue, but two linearly independent eigenvectors?

Question

Can we have a 2×2 matrix with one single eigenvalue, but two linearly independent eigenvectors? Is this possible? If so, how?

Thanks for the help!

Answer 1

$$\huge I_{2\times 2}{}{}{}{}{}{}$$

Answer 2

If you remember eigendecomposition, you can write a matrix as RUR^-1, where R is the matrix of eigen-vectors, and U is a diagonal matrix containing the eigenvalues. Thus you can plug the linearly independent eigenvectors you want into R, as well as the single eigenvalue you want into U.