91Ó°ÊÓ

True or False If a linear programming problem has a solution, it is located at a corner point of the graph of the feasible points.

True or False Matrix addition is commutative.

If the only solution to a system of two linear equations containing two variables is \(x=3, y=-2,\) then the graphs of the lines in the system intersect at the point ______.

Which statement describes the system of equations represented by \(\left[\begin{array}{rrr|r}1 & 5 & -2 & 3 \\ 0 & 1 & 3 & -2 \\ 0 & 0 & 0 & 5\end{array}\right] ?\) (a) The system has one solution. (b) The system has infinitely many solutions. (c) The system has no solution. (d) The number of solutions cannot be determined.

Multiple Choice If a system of two linear equations in two variables is inconsistent, then the graphs of the lines in the system are ________. (a) intersecting (b) parallel (c) coincident (d) perpendicular

To find the product \(A B\) of two matrices \(A\) and \(B,\) which statement must be true? (a) The number of columns in \(A\) must equal the number of rows in \(B\). (b) The number of rows in \(A\) must equal the number of columns in \(B\). (c) \(A\) and \(B\) must have the same number of rows and the same number of columns. (d) \(A\) and \(B\) must both be square matrices.

Solve each linear programming problem. Maximize \(z=2 x+y\) subject to the constraints \(x \geq 0, \quad y \geq 0, \quad x+y \leq 6, \quad x+y \geq 1\)

Solve each linear programming problem. Minimize \(z=2 x+5 y\) subject to the constraints \(x \geq 0, \quad y \geq 0, \quad x+y \geq 2, \quad x \leq 5, \quad y \leq 3\)

Determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. $$ \frac{x(x-1)}{(x+4)(x-3)} $$

Graph each equation of the system. Then solve the system to find the points of intersection. $$ \left\\{\begin{aligned} x^{2}+y^{2} &=10 \\ y &=x+2 \end{aligned}\right. $$