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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1:50 minutes

Problem 31

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. x + 3y + 4z = - 3x + 2y + 3z = - 2x + 4y + 3z = - 6

Verified step by step guidance

Identify the coefficients of each variable in the system of equations.

Construct the coefficient matrix A using the identified coefficients.

Construct the variable matrix X using the variables x, y, and z.

Construct the constant matrix B using the constants from the right-hand side of the equations.

Write the matrix equation in the form 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. The goal is to find the values of these variables that satisfy all equations simultaneously. In this case, the system includes three equations with three variables: x, y, and z.

Matrix Representation

Matrix representation of a linear system involves expressing the system in the form AX = B, where A is the coefficient matrix containing the coefficients of the variables, X is the column matrix of the variables, and B is the column matrix of constants. This format simplifies the process of solving the system using matrix operations.

Coefficient and Constant Matrices

The coefficient matrix A is formed by taking the coefficients of the variables from each equation and arranging them in a matrix format. The constant matrix B is created from the constant terms on the right side of the equations. Understanding how to construct these matrices is essential for converting a linear system into matrix form.