Exam 6: Systems and Matrices

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { r r } 6 & - 5 \\- 3 & 5\end{array} \right] \text { and } \left[ \begin{array} { c c } \frac { 1 } { 3 } & \frac { 1 } { 3 } \\\frac { 1 } { 5 } & \frac { 2 } { 5 }\end{array} \right]$

A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 95 black, 100 white and 80 red wires. How many of each type of cable were made?

Find the cofactor of the indicated element. $\mathrm{a}_{21}$ $\left|\begin{array}{rrr}5 & 2 & 1 \\-3 & 0 & 1 \\1 & 5 & 2\end{array}\right|$

Find the matrix product when possible. -Given $A = \left[ \begin{array} { r r } 1 & - 2 \\ 4 & 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 0 & - 1 \\ 5 & 4 \end{array} \right]$ , find $A B$ and $B A$ .

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - xy=72 x+y=-17

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } - 3 & - 2 \\0 & 5\end{array} \right]$

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?

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

Use a graphing calculator to find the inverse of the matrix. Give five decimal places, if necessary. - $A = \left[ \begin{array} { r r } \frac { 4 } { 3 } & 52 \\\sqrt { 21 } & 8.754\end{array} \right]$

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=1 y+z=4 z-w=1

Solve the system by elimination. 7x + 9y = -7 -4x + 3y = 4

Find the value of the determinant. $\left| \begin{array} { r r r } 5 & - 2 & 3 \\0 & 8 & 5 \\0 & 0 & - 6\end{array} \right|$

Provide an appropriate response. -Indicate whether the following statement is Interchanging corresponding rows and columns of a matrix changes the sign of the determinant of the matrix.

Find the matrix product when possible. -Given $A = \left[ \begin{array} { r r } 1 & - 2 \\ - 5 & 4 \end{array} \right]$ , find $A ^ { 3 }$ .

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r r } 6 & 5 & 18 \\ 5 & - 2 & 7 \\ 1 & 2 & 3 \end{array} \right] ; - 6$ times row 3 added to row 1

Choose the one alternative that best completes the statement or answers the question. Graph the inequality. $y \geq|x+6|$

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

Which of the following properties do not hold for matrix multiplication? (i) Associative property (ii) Commutative property (iii) Distributive property (iv) Zero-factor property (If the product of two matrices is a Zero matrix, then one of the factors must be a zero matrix.)

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } 5 & 5 \\- 4 & 0\end{array} \right]$

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { r r r } 1 & - 1 & 2 \\- 3 & - 2 & 4 \\- 1 & 1 & 1\end{array} \right] \text { and } \left[ \begin{array} { r r r } 2 & - 1 & 0 \\- 1 & 1 & - 2 \\1 & 0 & - 1\end{array} \right]$