Key Terms Chapter 04: Systems of Linear Equations
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| 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 |
|---|---|---|---|---|---|
| (Eg. "Genetic, Hereditary, DNA ...") | (Eg. "Relating to genes or heredity") |  | The infamous double helix | https://bio.libretexts.org/ | CC-BY-SA; Delmar Larsen |
| Word(s) | Definition | Image | Caption | Link | Source |
|---|---|---|---|---|---|
| break-even point | The point at which the revenue equals the costs is the break-even point; \(C(x)=R(x)\). | ||||
| coincident lines | Coincident lines have the same slope and same \(y\)-intercept. | ||||
| complementary angles | Two angles are complementary if the sum of the measures of their angles is \(90\) degrees. | ||||
| consistent and inconsistent systems | Consistent 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 function | The cost function is the cost to manufacture each unit times \(x\), the number of units manufactured, plus the fixed costs; \(C(x) = (\text{cost per unit})x+ \text{fixed costs}\). | ||||
| determinant | Each square matrix has a real number associated with it called its determinant. | ||||
| matrix | A matrix is a rectangular array of numbers arranged in rows and columns. | ||||
| minor of an entry in a \(3×3\) determinant | The 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. | ||||
| revenue | The 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 form | A 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 equations | Solutions 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 variables | The 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 matrix | A square matrix is a matrix with the same number of rows and columns. | ||||
| supplementary angles | Two angles are supplementary if the sum of the measures of their angles is \(180\) degrees. | ||||
| system of linear equations | When two or more linear equations are grouped together, they form a system of linear equations. | ||||
| system of linear inequalities | Two or more linear inequalities grouped together form a system of linear inequalities. |