Exam 6: Systems and Matrices

$\text { Let } A = \left[ \begin{array} { r r } 1 & - 4 \\4 & 6\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 1 & - 4 \\4 & 6\end{array} \right]$ Does the matrix A - B have an inverse?

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. -3 =1 4+3 =19

Which method should be used to solve the system? Explain your answer, including a description of the first step. - +=81 -5x-y=1

Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary. - $x - \sqrt { 2 } y = 3.7$ $2.85 x + y = - 8.23$

Use a graphing calculator to find the inverse of the matrix. Give five decimal places, if necessary. - $A = \left[ \begin{array} { c c c } 1 / 3 & 2 / 7 & 4 / 5 \\17 / 11 & 5 & 0 \\18 / 13 & - 5 / 6 & 8 / 7\end{array} \right]$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { r r r } - 8 & 8 & x \\1 & y & 3\end{array} \right] = \left[ \begin{array} { r r r } m & 8 & 2 \\n & - 3 & p\end{array} \right]$

Solve the system by substitution. - x-7y =6 x =8y

Solve the equation for x. $\left| \begin{array} { r r r } 0 & 0 & x \\- 4 & x & - 2 \\1 & 1 & x\end{array} \right| = 4$

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. y=|x| 2x-y=-15

Evaluate the determinant. $\left| \begin{array} { l l l l } 3 & 8 & 9 & 7 \\3 & 9 & 9 & 8 \\9 & 0 & 0 & 4 \\1 & 1 & 3 & 2\end{array} \right|$

Provide an appropriate response. -Let $\mathrm { P }$ be a $3 \times 3$ matrix that has a multiplicative inverse. Which of the following statements are false? (Let 0 represent the $3 \times 3$ zero matrix.) (i) $0 \cdot \mathrm { P } = 0$ (ii) $\mathrm { PP } - 1 = 0$ (iii) $\mathrm { P } ^ { - 1 } \mathrm { P } = \mathrm { I } _ { 3 }$ (iv) $\mathrm { PP } ^ { - 1 } = \mathrm { P }$

Provide an appropriate response. -Fill in the blanks to complete the statement. For a system of 5 equations and 5 unknowns, the corresponding augmented matrix will have _______ rows and _______ columns.

Find the partial fraction decomposition for the rational expression. $\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - $\mathrm { A }$ is $2 \times 1 ; \mathrm { B }$ is $1 \times 1$ .

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. y=(x+8) y=

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. 2-2=10 2+4=34

Provide an appropriate response. -Suppose that $\mathrm { A }$ is an $\mathrm { m } \times \mathrm { n }$ matrix and $\mathrm { B }$ is a $\mathrm { p } \times \mathrm { q }$ matrix. Under what conditions will the sum $\mathrm { A } + \mathrm { B }$ exist?

Solve the system by substitution. - x+y=-2 x-y=-8

Solve the system by using the inverse of the coefficient matrix. - -3x-y-8z=-36 -6x-7z=-34 5y+z=9