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

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

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1:29 minutes

Problem 1

Textbook Question

In Exercises 1–8, write the augmented matrix for each system of linear equations.

Verified step by step guidance

Identify the coefficients of each variable and the constants in the system of linear equations.

Write the coefficients of the variables in a matrix form, aligning them according to their respective variables.

Include the constants from the right-hand side of the equations as an additional column in the matrix.

Construct the augmented matrix by combining the coefficient matrix and the constants column.

Double-check the augmented matrix to ensure all coefficients and constants are correctly placed.

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Key Concepts

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

Augmented Matrix

An augmented matrix is a matrix that represents a system of linear equations, where each row corresponds to an equation and each column corresponds to the coefficients of the variables, along with an additional column for the constants on the right side of the equations. This format allows for efficient manipulation and solution of the system using matrix operations.

Linear Equations

Linear equations are mathematical statements that express a relationship between variables in which each term is either a constant or the product of a constant and a single variable. In the context of a system of equations, these equations can be solved simultaneously to find the values of the variables that satisfy all equations in the system.

Row Operations

Row operations are techniques used to manipulate the rows of a matrix to simplify it or to solve a system of equations. The three primary row operations are swapping two rows, multiplying a row by a non-zero scalar, and adding or subtracting the multiple of one row to another. These operations are fundamental in transforming an augmented matrix into row-echelon form or reduced row-echelon form.