Exam 10: Systems and Matrices

Solve the problem. -Bob fenced in a rectangular garden in his yard. The length of the rectangle is $7 \mathrm { ft }$ longer than the width and the perimeter is $122 \mathrm { ft }$ . What is the width of the rectangle?

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - +xy+=19 x+y=2

Find the indicated matrix. -Let $A = \left[ \begin{array} { l l } - 5 & 2 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]$ . Find $3 A + 4 B$ .

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. - x-y+2z+w=4 y+z=4 z-w=3

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l } - 2 & 6 \\- 3 & 6\end{array} \right]$

Solve the problem. -The following table shows the number of rectifiers, in thousands, produced by Allied Electronics 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 $b$ ? Year Number of rectifiers (in thousands) 0 12 3 69 5 137

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

Find the matrix product when possible. -Le Boulangerie, a bakery, sells four main items: sweet rolls, bread, cakes, and pies. The amount of e. ingredient (in cups, except for eggs) required for these items is given by matrix A. ach441) The cost (in cents) for each ingredient when purchased in large lots or small lots is given in matrix B. Use matrix multiplication to find a matrix giving the comparative cost per bakery item for the two purchase options.

Find the matrix product when possible. - $\left[ \begin{array} { r r } - 1 & 3 \\1 & 4\end{array} \right] \left[ \begin{array} { l l l } 0 & - 2 & 5 \\1 & - 3 & 2\end{array} \right]$

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

Find the matrix product when possible. - $\left[ \begin{array} { l l l } - 9 & 2 & 8 \end{array} \right] \left[ \begin{array} { r } 4 \\ 0 \\ - 3 \end{array} \right]$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 8 & - 5 & 4 \\15 & - 9 & 8 \\7 & - 4 & 4\end{array} \right]$

Provide an appropriate response. -Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with $x$ -intercepts at $( - 9,0 )$ and $( 9,0 )$ , and $y$ -intercepts at $( 0,3 )$ and $( 0 , - 3 )$ ?

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

Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants. - x+ay= x+by=

Evaluate the determinant. - $\left| \begin{array} { r r r } 5 & - 7 & 3 \\0 & 9 & 1 \\0 & 0 & - 8\end{array} \right|$

Find the value of the determinant. - $\left| \begin{array} { l l } a & b \\b & a\end{array} \right|$

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x + 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } > 16$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - xy=1 42x-y=-1

Write the augmented matrix for the system. Do not - 9x+4y =-10 2y =4