Solving Systems by Matrices

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved simultaneously.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

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

You can represent a system of equations in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

Front

What is the coefficient matrix in a system of equations?

Back

The matrix that contains the coefficients of the variables in the system.

Front

What is the augmented matrix?

Back

A matrix that includes the coefficients of the variables and the constants from the equations.

Front

What is Gaussian elimination?

Back

A method for solving systems of linear equations by transforming the augmented matrix into row echelon form.

Front

What is the row echelon form of a matrix?

Back

A form where all non-zero rows are above any rows of all zeros, and the leading coefficient of a non-zero row is always to the right of the leading coefficient of the previous row.

Front

What is back substitution?

Back

A method used to solve a system of equations after obtaining the row echelon form, by substituting known values back into the equations.

Front

What does it mean for a system to be consistent?

Back

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