Find the eigen value and eigen vectors
a. A = [1 1 0; 0 1 1]


To find the eigenvalues and eigenvectors of matrix \( A \), we follow these steps:

### Matrix:
\[
A = \begin{bmatrix}
1 & 1 & 0 \\
0 & 1 & 1
\end{bmatrix}
\]

Since this is a \( 2 \times 3 \) matrix (rectangular), it doesn't have the same set of eigenvalues and eigenvectors as a square matrix would. Eigenvalues and eigenvectors are typically defined for square matrices because they relate to how a matrix can be factored into components based on its characteristic polynomial, and for that, we need a square matrix.

Would you like to find another type of factorization for this matrix, or would you prefer an explanation about why eigenvalues and eigenvectors are only well-defined for square matrices? 

Here are some follow-up questions to expand on this:

1. Would you like to calculate the singular value decomposition (SVD) of this rectangular matrix?
2. Should we try another square matrix example for eigenvalue/eigenvector calculation?
3. Would you like a discussion on matrix transformations in general?
4. Should we explore how non-square matrices can be used in systems of equations?
5. Are you interested in learning how rectangular matrices are used in applications such as machine learning?

**Tip:** Eigenvalues and eigenvectors are powerful tools for understanding matrix behavior, but they are only defined for square matrices.

Find the eigenvalue and eigenvectors for matrix A = [1 1 0; 0 1 1]

Understand why eigenvalues and eigenvectors are only defined for square matrices and explore alternative approaches like singular value decomposition for rectangular matrices like A = [1 1 0; 0 1 1]. Suitable for undergraduate-level students studying linear algebra.

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