---
title: "LACS.PAR.8: Eigenvalue Real-Life Applications (Georgia Mathematics standard)"
code: LACS.PAR.8
cite_as: Georgia Standards of Excellence, Mathematics, LACS.PAR.8
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/LACS.PAR.8
md_url: https://georgiahomeroom.org/standards/code/LACS.PAR.8.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/LACS.PAR.8.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# LACS.PAR.8: Eigenvalue Real-Life Applications

Solve contextual, mathematical problems using eigenvalues and eigenvectors to explain real-life phenomena.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- Use and apply determinants.
  - **LACS.PAR.8.1**: Evaluate the determinant of a matrix along any row or column and use a recursive procedure for evaluating a determinant for matrices larger than 3-by-3.
  - **LACS.PAR.8.2**: Justify properties of the determinant.
  - **LACS.PAR.8.3**: Calculate the determinant of the product of two matrices; calculate the determinant of the transpose of a matrix.
  - **LACS.PAR.8.4**: Determine if a matrix has a nonzero determinant and extend the nonzero determinant property to problems involving linear dependency, rank, and matrix inverses.
  - **LACS.PAR.8.5**: Extend the definition and geometric interpretation of the cross product to *n* – 1 vectors in *n* dimensions.
  - **LACS.PAR.8.6**: Use Cramer’s Rule to solve a system of linear equations.
- Find and apply eigenvalues and eigenvectors.
  - **LACS.PAR.8.7**: Find the characteristic polynomial of a matrix and interpret the characteristic polynomial geometrically.
  - **LACS.PAR.8.8**: Find the eigenvalues and eigenvectors of a matrix and interpret them geometrically.
  - **LACS.PAR.8.9**: Use a basis of eigenvectors to create a change of basis matrix.
  - **LACS.PAR.8.10**: Find the dimension of the eigenspace corresponding to the eigenvalues of a symmetric matrix.
  - **LACS.PAR.8.11**: Determine an orthogonal matrix that diagonalizes a given matrix.
  - **LACS.PAR.8.12**: Apply eigenvalues and eigenvectors to problems in context.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.