Exam 9: Systems and Matrices

Use a graphing calculator to find the inverse of the matrix. Give five decimal places, if necessary. - $A = \left[ \begin{array} { l l } \sqrt { 3 } & - 4 \\\frac { 2 } { 7 } & 0.932\end{array} \right]$

Graph the inequality. - $(x+3)^{2}+(y-5)^{2} \leq 9$

Solve the problem using matrices. -Ellen wishes to mix candy worth $\$ 1.66$ per pound with candy worth $\$ 7.29$ per pound to form 27 pounds of a mixture worth $\$ 5.41$ per pound. How many pounds of the more expensive candy should she use?

Find the partial fraction decomposition for the rational expression. - $\frac { 6 x ^ { 3 } - 33 x ^ { 2 } + 51 x - 13 } { ( x - 2 ) ^ { 3 } ( x + 3 ) }$

Find the matrix product when possible. - $\left[ \begin{array} { r r r } - 6 & 1 & 8 \\ - 9 & 2 & - 9 \\ 6 & - 3 & 3 \end{array} \right] \left[ \begin{array} { r r r } - 9 & 1 & - 9 \\ 6 & - 8 & 5 \\ - 6 & 4 & - 4 \end{array} \right]$

Provide an appropriate response. -Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $\left[ \begin{array} { r r r | r } 1 & - 9 & 1 & 4 \\0 & - 1 & - 13 & - 8 \\0 & - 3 & - 2 & - 11\end{array} \right]$ What row operation would you perform next?

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$

Perform the operation or operations when possible. - $\left[ \begin{array} { r } 3 \\- 1 \\- 4\end{array} \right] + \left[ \begin{array} { r } - 5 \\1 \\7\end{array} \right]$

Find the dimension of the matrix. - $\left[ \begin{array} { r r r r r } - 2 & 6 & 2 & - 9 & - 8 \\1 & 5 & 2 & 2 & 9 \\- 2 & - 3 & 4 & 2 & 6\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Let $A = \left[ \begin{array} { r r } 3 & 6 \\ - 6 & 2 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 6 & - 6 \\ 6 & - 2 \end{array} \right]$ Does the matrix $\mathrm { A } + \mathrm { B }$ have an inverse?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Let $A = \left[ \begin{array} { l l } d & 0 \\ 0 & f \end{array} \right]$ , where $d$ and $f$ are nonzero constants. Find $A ^ { - 1 }$ .

Find the partial fraction decomposition for the rational expression. - $\frac { 2 x ^ { 3 } - 3 x ^ { 2 } - 2 x + 27 } { x ^ { 2 } + x - 2 }$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y= +=5.7

Provide an appropriate response. -Suppose that you are solving a system of three linear equations and have evaluated $\mathrm { D } ^ { 2 } \mathrm { D } _ { \mathrm { X } } , \mathrm { D } _ { \mathrm { y } }$ , and $\mathrm { D } _ { \mathrm { Z } }$ . Under what condition does Cramer's rule not apply?

Solve the system in terms of the arbitrary variable x. - $x - 3 y + z = 13$ $3 x - y - z = 3$

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

Solve the system by substitution. - x-3y =6 x =4y

For the equation, determine the constants A and B that make the equation an identity. - $\frac { x - 5 } { x ^ { 2 } } = \frac { A } { x } + \frac { B } { x ^ { 2 } }$

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } 6.6 & - 4.8 & 3 \\- 8.1 & - 5.3 & - 3.7 \\2.9 & 4.7 & 1.5\end{array} \right|$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - +=100 x+5y=2