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9.10.1: Key Terms

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    Key Terms

    addition method
    an algebraic technique used to solve systems of linear equations in which the equations are added in a way that eliminates one variable, allowing the resulting equation to be solved for the remaining variable; substitution is then used to solve for the first variable
    augmented matrix
    a coefficient matrix adjoined with the constant column separated by a vertical line within the matrix brackets
    break-even point
    the point at which a cost function intersects a revenue function; where profit is zero
    coefficient matrix
    a matrix that contains only the coefficients from a system of equations
    a set of numbers aligned vertically in a matrix
    consistent system
    a system for which there is a single solution to all equations in the system and it is an independent system, or if there are an infinite number of solutions and it is a dependent system
    cost function
    the function used to calculate the costs of doing business; it usually has two parts, fixed costs and variable costs
    Cramer’s Rule
    a method for solving systems of equations that have the same number of equations as variables using determinants
    dependent system
    a system of linear equations in which the two equations represent the same line; there are an infinite number of solutions to a dependent system
    a number calculated using the entries of a square matrix that determines such information as whether there is a solution to a system of equations
    an element, coefficient, or constant in a matrix
    feasible region
    the solution to a system of nonlinear inequalities that is the region of the graph where the shaded regions of each inequality intersect
    Gaussian elimination
    using elementary row operations to obtain a matrix in row-echelon form
    identity matrix
    a square matrix containing ones down the main diagonal and zeros everywhere else; it acts as a 1 in matrix algebra
    inconsistent system
    a system of linear equations with no common solution because they represent parallel lines, which have no point or line in common
    independent system
    a system of linear equations with exactly one solution pair ( x,y ) ( x,y )
    main diagonal
    entries from the upper left corner diagonally to the lower right corner of a square matrix
    a rectangular array of numbers
    multiplicative inverse of a matrix
    a matrix that, when multiplied by the original, equals the identity matrix
    nonlinear inequality
    an inequality containing a nonlinear expression
    partial fraction decomposition
    the process of returning a simplified rational expression to its original form, a sum or difference of simpler rational expressions
    partial fractions
    the individual fractions that make up the sum or difference of a rational expression before combining them into a simplified rational expression
    profit function
    the profit function is written as P(x)=R(x)C(x), P(x)=R(x)C(x), revenue minus cost
    revenue function
    the function that is used to calculate revenue, simply written as R=xp, R=xp, where x= x= quantity and p= p= price
    a set of numbers aligned horizontally in a matrix
    row operations
    adding one row to another row, multiplying a row by a constant, interchanging rows, and so on, with the goal of achieving row-echelon form
    row-echelon form
    after performing row operations, the matrix form that contains ones down the main diagonal and zeros at every space below the diagonal
    two matrices A A and B B are row-equivalent if one can be obtained from the other by performing basic row operations
    scalar multiple
    an entry of a matrix that has been multiplied by a scalar
    solution set
    the set of all ordered pairs or triples that satisfy all equations in a system of equations
    substitution method
    an algebraic technique used to solve systems of linear equations in which one of the two equations is solved for one variable and then substituted into the second equation to solve for the second variable
    system of linear equations
    a set of two or more equations in two or more variables that must be considered simultaneously.
    system of nonlinear equations
    a system of equations containing at least one equation that is of degree larger than one
    system of nonlinear inequalities
    a system of two or more inequalities in two or more variables containing at least one inequality that is not linear

    9.10.1: Key Terms is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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