Systems, Matrices, and Inequalities flashcards

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In Systems of Equations in Two and Three Variables, what does common solution mean?Systems of Equations in Two and Three Variables: A simultaneous assignment of unknowns.
Does satisfying one equation suffice?Systems of Equations in Two and Three Variables: No, check every equation in the system.
In Systems of Equations in Two and Three Variables, what does elimination mean?Systems of Equations in Two and Three Variables: A variable-removal method for systems.
Why scale every term of a row?Systems of Equations in Two and Three Variables: Scaling only part of an equation changes its solutions.
In Systems of Equations in Two and Three Variables, what does consistency and meaning mean?Systems of Equations in Two and Three Variables: Classification of simultaneous constraints.
Why check contextual restrictions?Systems of Equations in Two and Three Variables: A mathematical answer may be impossible in the real problem.
In Matrices and Operations, what does matrix dimensions mean?Matrices and Operations: The shape and compatibility of a rectangular array.
What shape is an (m×n)(n×p) product?Matrices and Operations: m×p.
In Matrices and Operations, what does addition and scalar multiplication mean?Matrices and Operations: Entrywise addition and scalar scaling.
Can a 2×3 matrix be added to a 3×2 matrix?Matrices and Operations: No, their shapes differ.
In Matrices and Operations, what does matrix multiplication mean?Matrices and Operations: The row-column rule for a product entry.
Is AB always BA?Matrices and Operations: No, order can change or make a product undefined.
In Solving Systems with Matrices, what does augmented matrix mean?Solving Systems with Matrices: A coefficient table with a separated constant column.
Why keep variable order fixed?Solving Systems with Matrices: A swapped column would represent a different system.
In Solving Systems with Matrices, what does elementary row operations mean?Solving Systems with Matrices: Reversible transformations of a linear system.
Why prohibit scaling a row by zero?Solving Systems with Matrices: It destroys information and cannot be reversed.
In Solving Systems with Matrices, what does back-substitution mean?Solving Systems with Matrices: Recovering unknowns from an equivalent row-reduced system.
Why check the original equations?Solving Systems with Matrices: Entry or arithmetic errors can occur during row operations.
In Systems of Inequalities, what does boundary lines mean?Systems of Inequalities: Graphical boundaries of inequality regions.
When is the boundary included?Systems of Inequalities: When ≤ or ≥ is used.
In Systems of Inequalities, what does feasible region mean?Systems of Inequalities: The common allowable region of all constraints.
Does satisfying one inequality suffice?Systems of Inequalities: No, every constraint must hold.
In Systems of Inequalities, what does checking points mean?Systems of Inequalities: Algebraic verification of a graph solution.
Why check boundary points separately?Systems of Inequalities: Strict signs exclude equality but inclusive signs allow it.
In Linear Optimization in Context, what does objective function mean?Linear Optimization in Context: A target expression to maximize or minimize.
Why state objective units?Linear Optimization in Context: They tell what an extreme value actually measures.
In Linear Optimization in Context, what does feasible vertices mean?Linear Optimization in Context: Candidate extremum points under linear constraints.
Can an entire edge tie?Linear Optimization in Context: Yes, when the objective is parallel to that edge.
In Linear Optimization in Context, what does model limitations mean?Linear Optimization in Context: Restrictions beyond a continuous linear model.
Why not round an optimum automatically?Linear Optimization in Context: Rounding can violate one of the constraints.