Exam 9: Systems and Matrices

Solve the problem. -Twice the water flow in the hot-water pipe is the same as three times the flow in the cold-water pipe. The combined flow is 1500 L/hr. What is the flow in each pipe?

Find the cofactor of the indicated element. - $\mathrm{a} 13$ $\left|\begin{array}{rrr}-2 & -1 & 0 \\4 & 1 & 3 \\1 & 2 & 2\end{array}\right|$

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - x+y=-4 x+y=-2

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - $a x + b y = \frac { a } { b }$ $x + y = \frac { 1 } { a }$

Solve the system by substitution. - x-3y=0 4x-3y=-18

Provide an appropriate response. -For any augmented matrix of a system of linear equations, which of the following row transformations will not necessarily result in a matrix of an equivalent system? (i) Adding to the elements of any row a multiple of the corresponding elements of another row. (ii) Interchanging any two columns. (iii) Multiplying the elements of any row by the corresponding elements of another row. (iv) Multiplying the elements of any row by any nonzero number.

Solve the problem. -Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $90 for 3 days and 300 miles, while Mary was charged $162 for 5 days and 600 miles. What does Best Rental Charge per day and per mile?

Solve the problem. -Find the equation of the circle, written in the form $x ^ { 2 } + y ^ { 2 } + a x + b y + c = 0$ , passing through the points $( 11,6 ) , ( 6,1 )$ , and $( 9,10 )$ .

Solve the problem. -A rectangular plot has area $126 \mathrm { yd } ^ { 2 }$ with a perimeter of $46 \mathrm { yd }$ . What is the length of the longest side?

Graph the inequality. - $-2 x-4 y \leq 8$

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - -4x-7y-z=-67 x+6y-2z=20 9x+y+z=67

Solve the equation for x. - $\left| \begin{array} { l l } x & 3 \\ 2 & 1 \end{array} \right| = 6$

Provide an appropriate response. -If the graphs of a system of two equations are both circles, what are the possible numbers of solutions (with real coordinates) of this system?

Find the matrix product when possible. - $\left[ \begin{array} { r r r } 1 & 3 & - 3 \\2 & 0 & 5\end{array} \right] \left[ \begin{array} { r r } 3 & 0 \\- 3 & 1 \\0 & 5\end{array} \right]$

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - ax+y=b x+by=a

Solve the problem. -Find the dimensions of a rectangular enclosure with perimeter $40 \mathrm { yd }$ and area $91 \mathrm { yd } ^ { 2 }$ .

Solve the problem. -The following table shows the number of dog collars, in thousands, produced by Allied Pet Products in the three years considered. For a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ that fits this data, what is the value of $c$ ?

Graph the inequality. - $(x-4)^{2}+(y+3)^{2} \leq 16$

Find the partial fraction decomposition for the rational expression. - $\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$

Graph the inequality. - $3 x+4 y \leq 12$