Solving Systems by Matrices

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is a matrix?

Back

A rectangular array of numbers arranged in rows and columns.

Front

How do you represent a system of equations using matrices?

Back

By creating an augmented matrix that includes the coefficients and constants of the equations.

Front

What is the augmented matrix for the system: 5x + 8y = -12 and 3x + 5y = -7?

Back

[5 8 | -12; 3 5 | -7]

Front

What is the purpose of row operations in matrix algebra?

Back

To simplify the matrix to find solutions to the system of equations.

Front

What are the three types of row operations?

Back

1. Swapping two rows, 2. Multiplying a row by a non-zero scalar, 3. Adding or subtracting rows.

Front

What does it mean if a system of equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How can you determine if a system of equations has a unique solution?

Back

If the lines represented by the equations intersect at exactly one point.