Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

College Algebra

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

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1:44 minutes

Problem 29

Textbook Question

In Exercises 29 - 32, write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix. 6x + 5y = 135x + 4y = 10

Verified step by step guidance

Identify the coefficients of the variables in each equation.

Construct the coefficient matrix A using the coefficients from the equations.

Construct the variable matrix X using the variables from the equations.

Construct the constant matrix B using the constants from the equations.

Combine the matrices to form the matrix equation AX = B.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Linear Systems

A linear system consists of two or more linear equations involving the same set of variables. In this case, the system includes the equations 6x + 5y = 13 and 5x + 4y = 10. The goal is to find values for the variables that satisfy all equations simultaneously.

Matrix Representation

A matrix representation of a linear system organizes the coefficients of the variables and the constants into matrices. The system can be expressed in the form AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. This format simplifies the process of solving the system using matrix operations.

Coefficient and Constant Matrices

In the matrix equation AX = B, the coefficient matrix A contains the coefficients of the variables from the linear equations, while the constant matrix B contains the constants from the right-hand side of the equations. For the given system, A would be [[6, 5], [5, 4]] and B would be [[13], [10]]. Understanding how to construct these matrices is crucial for solving the system.