# Find Eigenvalues & Basis C2 Matrix: Help!

• MHB
• wefweff
In summary, eigenvalues and eigenvectors are concepts in linear algebra used to describe the behavior of linear transformations. To find the eigenvalues of a matrix, you need to solve the characteristic equation, and to find the basis for a matrix, you need to find the eigenvectors. Finding eigenvalues and basis is important because it helps us understand the behavior of a given matrix, and can be useful in various applications such as data analysis and image processing.
wefweff
Good afternoon to all again! I'm solving last year's problems and can't cope with this problem:( help me to understand the problem and find a solution!

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That matrix does NOT have real eigenvalues. The eigenvalues are $-5\pm i$

## 1. What is an eigenvalue?

An eigenvalue is a scalar value that represents the scaling factor of an eigenvector when a linear transformation is applied to it. In simpler terms, it is a special number associated with a matrix that describes how the matrix stretches or compresses a vector.

## 2. How do I find eigenvalues of a matrix?

To find eigenvalues of a matrix, you need to solve the characteristic equation det(A - λI) = 0, where A is the given matrix and λ is the eigenvalue. This will give you one or more eigenvalues for the matrix.

## 3. What is a basis in linear algebra?

A basis is a set of linearly independent vectors that span a vector space. It is the minimal set of vectors needed to represent all other vectors in that space. In other words, any vector in the vector space can be written as a linear combination of the basis vectors.

## 4. How do I find the basis of a matrix?

To find the basis of a matrix, you need to first find the eigenvalues of the matrix. Then, for each eigenvalue, find the corresponding eigenvectors. The set of all eigenvectors will form the basis of the matrix.

## 5. Why is finding eigenvalues and basis important?

Finding eigenvalues and basis is important because it helps us understand the behavior of a matrix and its effect on vectors. It is also used in various applications such as solving systems of differential equations, image compression, and data analysis.

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