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Questions and Answers
What is a region called when the graph of a system of constraints is a polygonal region?
What is a region called when the graph of a system of constraints is a polygonal region?
What do we call the point at which income equals cost?
What do we call the point at which income equals cost?
Break-Even Point
What type of matrix contains only the coefficients of a system of equations?
What type of matrix contains only the coefficients of a system of equations?
Variable Matrix
What is a system of equations that has at least one ordered pair that satisfies both equations?
What is a system of equations that has at least one ordered pair that satisfies both equations?
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What type of matrix contains the constants of a system?
What type of matrix contains the constants of a system?
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What is the name of the method that uses determinants to solve systems of linear equations?
What is the name of the method that uses determinants to solve systems of linear equations?
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What do we call a system of equations that has an infinite number of solutions?
What do we call a system of equations that has an infinite number of solutions?
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What is a square array of numbers or variables enclosed between two parallel lines called?
What is a square array of numbers or variables enclosed between two parallel lines called?
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What is the method for finding the determinant of a third-order matrix?
What is the method for finding the determinant of a third-order matrix?
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What are the dimensions of a matrix represented as?
What are the dimensions of a matrix represented as?
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What method eliminates one of the variables in a system of equations?
What method eliminates one of the variables in a system of equations?
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What do we call the intersection of the graphs in a system of constraints?
What do we call the intersection of the graphs in a system of constraints?
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What is a square matrix that, when multiplied by another matrix, equals the same matrix?
What is a square matrix that, when multiplied by another matrix, equals the same matrix?
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What do we call a system of equations with no ordered pair that satisfies both equations?
What do we call a system of equations with no ordered pair that satisfies both equations?
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What type of system of equations has exactly one solution?
What type of system of equations has exactly one solution?
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What are two matrices called when their product is the identity matrix?
What are two matrices called when their product is the identity matrix?
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What is any rectangular array of variables or constants in horizontal rows and vertical columns called?
What is any rectangular array of variables or constants in horizontal rows and vertical columns called?
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What is the matrix form used to represent a system of equations called?
What is the matrix form used to represent a system of equations called?
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What does it mean to seek optimal price or amount to minimize costs or maximize profits?
What does it mean to seek optimal price or amount to minimize costs or maximize profits?
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What is the solution of a system of equations in three variables called?
What is the solution of a system of equations in three variables called?
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What is a constant referred to as in mathematical terms?
What is a constant referred to as in mathematical terms?
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What is the process of multiplying any matrix by a constant called?
What is the process of multiplying any matrix by a constant called?
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What is the method for solving a system of equations where one equation is solved for one variable in terms of the other?
What is the method for solving a system of equations where one equation is solved for one variable in terms of the other?
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What do we call a system of inequalities that forms a region that is open?
What do we call a system of inequalities that forms a region that is open?
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What is a matrix that only contains the variables of a system of equations called?
What is a matrix that only contains the variables of a system of equations called?
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Study Notes
Matrix and Systems of Equations Vocabulary
- Bounded: Refers to a region defined by a system of constraints resulting in a polygonal area within a graph.
- Break-Even Point: The stage where total income matches total costs, indicating no profit or loss.
- Variable Matrix: Composed solely of coefficients from a system of equations, it represents the variables in matrix form.
- Consistent System: A set of equations that contains at least one solution, represented by an ordered pair satisfying both equations.
- Constant Matrix: This matrix holds the constants from a system of equations, distinct from coefficients.
- Cramer's Rule: A technique utilizing determinants to find the solutions for a set of linear equations.
- Dependent System: Characterized by having infinitely many solutions, indicating the equations represent the same line.
- Determinant: A square arrangement of numbers or variables, depicted between two parallel lines, pivotal in solving systems.
- Diagonal Rule: A method specifically used to calculate the determinant of a third-order matrix.
- Dimensions: The specification of a matrix's size represented as rows (m) by columns (n), noted as m x n.
Methods of Solving Equations and Matrix Operations
- Elimination Method: Involves manipulating equations to cancel out one variable, simplifying the system for resolution.
- Feasible Region: The outcome from the intersection of graph representations of constraints, indicating viable solutions.
- Identity Matrix: A square matrix that preserves the original matrix's value when multiplied; identified by the equation A*I=A.
- Inconsistent System: A scenario where no solution exists, meaning there is no ordered pair that satisfies the equations simultaneously.
- Independent System: This system has precisely one unique solution, indicating distinct intersection points of its equations.
- Inverse Matrices: Defined as two matrices that produce an identity matrix when multiplied together, crucial for solving equations.
- Matrix: Any rectangular array of elements (variables or constants), systematically organized in rows and columns.
- Matrix Equation: Represents a system of equations in matrix form, facilitating easier manipulation and solution finding.
Optimization and Specific Terms
- Optimize: The mathematical procedure of finding the best pricing or quantity to either minimize costs or maximize profits.
- Ordered Triple: The solution of a system of equations when dealing with three variables, denoted as (x, y, z).
- Scalar: Represents a constant factor that can modify matrices through multiplication.
- Scalar Multiplication: The process of multiplying each element of a matrix by a constant known as a scalar.
- Substitution Method: A solving technique where one equation is rearranged to substitute a variable into another equation.
- Unbounded: Describes a system of inequalities that creates an open region in graphing, implying no limitation on variable values.
- Coefficient Matrix: A matrix that includes only the coefficients of the variables from a system of equations, excluding constants.
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Description
Test your understanding of key vocabulary terms from Algebra 2 Chapter 3. This quiz focuses on important concepts such as bounded, break-even point, and variable matrix, providing brief definitions to enhance your learning experience. Perfect for revision or self-assessment in algebra.
