Solving Systems w/ Matrices

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.

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How do you write a system of equations as an augmented matrix?

Back

To write a system of equations as an augmented matrix, list the coefficients of the variables in each equation as rows and the constants as an additional column.

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the set of values for the variables that make all equations true.

Front

What is a consistent system of equations?

Back

A consistent system of equations has at least one solution.

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solutions.

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What is a dependent system of equations?

Back

A dependent system of equations has infinitely many solutions, as the equations represent the same line or plane.

Front

How can you determine if a system of equations has no solution?

Back

A system of equations has no solution if the equations represent parallel lines that never intersect.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the intersection point(s) of the lines or planes represented by the equations.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.