Chapter 6: Systems of Linear Equations and Matrices

Front

What is a system of linear equations?

Back

A system of linear equations is a collection of two or more linear equations involving the same set of variables.

Front

What is an augmented matrix?

Back

An augmented matrix is a matrix that represents a system of linear equations, including the coefficients of the variables and the constants from the equations.

Front

How do you convert a system of linear equations into an augmented matrix?

Back

To convert, write the coefficients of the variables in a matrix form and append the constants as an additional column.

Front

What does it mean for a system of linear equations to be consistent?

Back

A system is consistent if it has at least one solution.

Front

What does it mean for a system of linear equations to be inconsistent?

Back

A system is inconsistent if it has no solutions.

Front

What is the solution to a system of linear equations?

Back

The solution is the set of values for the variables that satisfy all equations in the system.

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

What is the purpose of using matrices in solving systems of linear equations?

Back

Matrices simplify the process of solving systems of equations, allowing for efficient calculations using methods like row reduction.

Front

What is row reduction?

Back

Row reduction is a method used to simplify a matrix to its row echelon form or reduced row echelon form to solve linear systems.

Front

What is the row echelon form of a matrix?

Back

A matrix is in row echelon form if all nonzero rows are above any rows of all zeros, and the leading coefficient of a nonzero row is to the right of the leading coefficient of the previous row.