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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.

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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 convert a system of linear equations into an augmented matrix?

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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.

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

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A system is inconsistent if it has no solutions.

Front

What is the solution to a system of linear equations?

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

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What is a matrix?

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

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

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

Front

What is row reduction?

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

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What is the row echelon form of a matrix?

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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.