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Key Terms Chapter 04: Systems of Linear Equations

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    102245
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    Example and Directions
    Words (or words that have the same definition)The definition is case sensitive(Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages](Optional) Caption for Image(Optional) External or Internal Link(Optional) Source for Definition
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    Glossary Entries
    Word(s)DefinitionImageCaptionLinkSource
    break-even pointThe point at which the revenue equals the costs is the break-even point; \(C(x)=R(x)\).    
    coincident linesCoincident lines have the same slope and same \(y\)-intercept.    
    complementary anglesTwo angles are complementary if the sum of the measures of their angles is \(90\) degrees.    
    consistent and inconsistent systemsConsistent system of equations is a system of equations with at least one solution; inconsistent system of equations is a system of equations with no solution.    
    cost functionThe cost function is the cost to manufacture each unit times \(x\), the number of units manufactured, plus the fixed costs; \(C(x) = (\text{cost per unit})x+ \text{fixed costs}\).    
    determinantEach square matrix has a real number associated with it called its determinant.    
    matrixA matrix is a rectangular array of numbers arranged in rows and columns.    
    minor of an entry in a \(3×3\) determinantThe minor of an entry in a \(3×3\) determinant is the \(2×2\) determinant found by eliminating the row and column in the \(3×3\) determinant that contains the entry.    
    revenueThe revenue is the selling price of each unit times \(x\), the number of units sold; \(R(x) = (\text{selling price per unit})x\).    
    row-echelon formA matrix is in row-echelon form when to the left of the vertical line, each entry on the diagonal is a \(1\) and all entries below the diagonal are zeros.    
    solutions of a system of equationsSolutions of a system of equations are the values of the variables that make all the equations true; solution is represented by an ordered pair \((x,y)\).    
    solutions of a system of linear equations with three variablesThe solutions of a system of equations are the values of the variables that make all the equations true; a solution is represented by an ordered triple \((x,y,z)\).    
    square matrixA square matrix is a matrix with the same number of rows and columns.    
    supplementary anglesTwo angles are supplementary if the sum of the measures of their angles is \(180\) degrees.    
    system of linear equationsWhen two or more linear equations are grouped together, they form a system of linear equations.    
    system of linear inequalitiesTwo or more linear inequalities grouped together form a system of linear inequalities.    
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