Solving Systems of Equations using Matrices (CFA)

Front

What is a Coefficient Matrix in a matrix equation?

Back

A Coefficient Matrix is a matrix that contains the coefficients of the variables in a system of equations.

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What is a Variable Matrix in a matrix equation?

Back

A Variable Matrix is a matrix that contains the variables of the system of equations.

Front

What is a Constant Matrix in a matrix equation?

Back

A Constant Matrix is a matrix that contains the constant terms from the equations.

Front

What is a Solution Matrix in a matrix equation?

Back

A Solution Matrix is a matrix that contains the solutions to the system of equations.

Front

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

Back

A consistent and dependent system has an infinite number of solutions, meaning the equations represent the same line.

Front

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

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines.

Front

How do you write a system of equations in matrix form?

Back

To write a system in matrix form, express it as AX = B, where A is the Coefficient Matrix, X is the Variable Matrix, and B is the Constant Matrix.

Front

What is the graphical representation of a consistent system of equations?

Back

The graphical representation of a consistent system is intersecting lines.

Front

What is the graphical representation of an inconsistent system of equations?

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The graphical representation of an inconsistent system is parallel lines.

Front

How do you solve a system of equations using the substitution method?

Back

To solve using substitution, solve one equation for one variable and substitute that expression into the other equation.