---
title: "LACS.PAR.4: Matrix Applications in Context (Georgia Mathematics standard)"
code: LACS.PAR.4
cite_as: Georgia Standards of Excellence, Mathematics, LACS.PAR.4
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/LACS.PAR.4
md_url: https://georgiahomeroom.org/standards/code/LACS.PAR.4.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/LACS.PAR.4.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.4: Matrix Applications in Context

Solve contextual, mathematical problems involving matrices to explain real-life phenomena.

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

## Expectations

- Use matrices to solve systems of linear equations.
  - **LACS.PAR.4.1**: Represent a linear system of three equations in three variables as an augmented matrix and reduce the matrix to row-echelon form.
  - **LACS.PAR.4.2**: Interpret the nature of the solution of a system from its row-echelon form, and if there are infinitely many solutions, express them as a vector equation.
  - **LACS.PAR.4.3**: Determine whether a vector is a linear combination of other given vectors; find the linear combination of vectors that results in a given vector.
  - **LACS.PAR.4.4**: Interpret linear dependence of vectors geometrically.
  - **LACS.PAR.4.5**: Find the kernel of a matrix and explore the relationship between the kernel, the orthogonality of the vectors in the kernel, and the linear dependence of the rows/columns.
- Operations on and with matrices.
  - **LACS.PAR.4.6**: Add two matrices, multiply a matrix by a scalar, find the transpose of a matrix.
  - **LACS.PAR.4.7**: Determine when matrix multiplication is defined, and if defined, multiply two matrices by considering the matrix product as a dot product of a group of vectors.
  - **LACS.PAR.4.8**: Determine when the inverse of a square matrix exists, and if it exists, find it by augmenting the identity matrix to the matrix and then use row operations.
  - **LACS.PAR.4.9**: Decompose a matrix into its symmetric and skew-symmetric parts; decompose a matrix into its LU factorization.
  - **LACS.PAR.4.10**: Solve a matrix equation using inverses; find all solutions to a matrix equation given one solution and the kernel.
- Solve applied problems involving matrices using programming.
  - **LACS.PAR.4.11**: Improve the simple authentication scheme over GF(2).
  - **LACS.PAR.4.12**: Show and explain how threshold secret sharing works in conjunction with Gaussian elimination through programming.
  - **LACS.PAR.4.13**: Write code utilizing error-correcting concepts.

## 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.