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What is the relationship between linear algebra and economics?
Many problems in economics can be modelled by a system of linear equations: equalities r inequalities. Such systems are best solved using matrix algebra.
When equations of linear systems have different slopes how many solutions does it have?
One solution
Do all linear quadratic systems have two solutions or one?
They will have 2 different solutions or 2 equal solutions and some times none depending on the value of the discriminant within the quadratic equation
In the graph of a linear inequality the shaded region above or below the line is called?
The shaded region above or below the line in the graph of a linear inequality is called the solution region. This region represents all the possible values that satisfy the inequality. Points within the shaded region are solutions to the inequality, while points outside the shaded region are not solutions.
How many solutions does linear equation in two variable have?
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Must solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Do solutions to systems of linear inequalities need to satisfy linear inequalities?
No. For example, the solution to x ≤ 4 and x ≥ 4 is x = 4.
How many solution sets do systems of linear inequalities have. Must solutions to systems of linear inequalities satisfy both inequalities. In what case might they not?
There is only one solution set. Depending on the inequalities, the set can be empty, have a finite number of solutions, or have an infinite number of solutions. In all cases, there is only one solution set.
How many solution sets do systems of linear inequalities have Must solutions to systems of linear inequalities satisfy both inequalities In what case might they not?
A solution to a linear inequality in two variables is an ordered pair (x, y) that makes the inequality a true statement. The solution set is the set of all solutions to the inequality. The solution set to an inequality in two variables is typically a region in the xy-plane, which means that there are infinitely many solutions. Sometimes a solution set must satisfy two inequalities in a system of linear inequalities in two variables. If it does not satisfy both inequalities then it is not a solution.
What is the relationship between linear algebra and economics?
Many problems in economics can be modelled by a system of linear equations: equalities r inequalities. Such systems are best solved using matrix algebra.
When equations of linear systems have different slopes how many solutions does it have?
One solution
How many solutions do systems of linear inequalities have?
They can have none, one or infinitely many.
Do solutions to systems of linear inequalities need to satify both inequalities?
If it is joined by an "and" it does. If it is joined by an "or" it does not.
Do all linear quadratic systems have two solutions or one?
They will have 2 different solutions or 2 equal solutions and some times none depending on the value of the discriminant within the quadratic equation
What is the solution to a linear equation?
The solution to a system on linear equations in nunknown variables are ordered n-tuples such that their values satisfy each of the equations in the system. There need not be a solution or there can be more than one solutions.
Why should you clear fractions to solve linear equalities?
You don't have to. Some people find that it makes subsequent calculations easier - but not all do.
