Exam 7: Systems of Equations and Matrices

Decide whether or not matrix A and matrix B are inverses. - $A = \left[ \begin{array} { r r } - 5 & - 1 \\6 & 0\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 0 & 1 / 6 \\- 1 & 5 / 6\end{array} \right]$

Decide whether or not matrix A and matrix B are inverses. - $A = \left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right]$

Write the augmented matrix associated with the system. - $\left\{ \begin{array} { r } - 2 x - 2 z = - 6 \\- 2 y + 6 z = 10 \\9 x + 7 y + 8 z = 32\end{array} \right.$

The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists. - $\left[ \begin{array} { r r r | r } 1 & - 1 & 1 & - 3 \\1 & 1 & 1 & 3 \\1 & 1 & - 1 & 1\end{array} \right]$

Use an inverse matrix to find the solution to the system. - $\left\{ \begin{aligned}4 x + 3 z & = 43 \\8 x + 6 y + 8 z & = 102 \\- 4 x - 6 y & = - 34\end{aligned} \right.$

The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists. - $\left[ \begin{array} { r r r | r } 1 & 0 & 0 & - 5 \\ 0 & 1 & 0 & 9 \\ 0 & 0 & 1 & 9 \end{array} \right]$

A company manufactures three types of cable. Cable A requires 3 black wires, 3 white wires, and 2 red wires. Cable B requires 1 black, 2 white, and 1 red. Cable C requires 2 black, 1 white, and 2 red. If 100 black wires, 110 White wires, and 90 red wires are required to complete an order, how many of each type of cable are in the Order?

A matrix has an inverse if and only if its determinant does not equal 0. Determine whether the given matrix has an inverse. - $\left[ \begin{array} { r r } 8 & 3 \\- 16 & - 6\end{array} \right]$

Write the augmented matrix associated with the system. - $\left\{ \begin{array} { l } 7 x + 5 y + 4 z = 65 \\4 x + 8 y + 4 z = 56 \\9 x + 8 y + 2 z = 93\end{array} \right.$

A trust account manager has $400,000 to be invested in three different accounts. The accounts pay 5%, 6%, and 10%, and the goal is to earn $32,000. Assuming that x dollars are invested at 5%, y dollars are invested at 6%,And z dollars are invested at 8%, what limits must there be on z so that all investment values are non-negative?

first two games of the season. Write a matrix containing the total number of points and rebounds for each of the starting five. Game 1 Points Rebounds Levy 20 3 Cowens 16 5 Williams 8 12 Miller 6 11 Jenkins 10 2 Game 2 Points Rebounds Levy 18 4 Cowens 14 3 Williams 12 9 Miller 4 10 Jenkins 10 3 A) $\left[ \begin{array} { l l } 5 & 62 \end{array} \right]$ В) $\left[ \begin{array} { r r } 7 & 38 \\ 30 & 8 \\ 21 & 20 \\ 21 & 10 \\ 5 & 20 \end{array} \right]$ C) $\left[ \begin{array} { r r } 38 & 7 \\ 30 & 8 \\ 20 & 21 \\ 10 & 21 \\ 20 & 5 \end{array} \right]$ D) $[ 625 ]$ Answer: C -Mike's Bait Shop sells three types of lures (discount, normal, and professional) at its three locations. The table below shows the number of lures of each type sold per day at each location. Lures Sold Discount Regular Professional Location I 16 100 30 Location II 16 90 36 Location III 60 120 40 The income per lure for discount, normal, and professional lures is $5, $9, and $12, respectively. Create two matrices To represent these data, and use matrix multiplication to find a matrix that gives the daily income at each Location.

The sum of a student's three scores is 224. If the first is 13 points more than the second, and the sum of the first two is 29 more than twice the third, then what was the first score?

Use an inverse matrix to find the solution to the system. - $\left\{ \begin{array} { l } - 3 x - 7 y - 2 z = - 43 \\- 9 x + 6 y + 5 z = 2 \\- 5 x - 7 y + 5 z = - 4\end{array} \right.$

The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists. - $\left[ \begin{array} { r r r | r } 5 & 2 & 1 & - 8 \\2 & - 3 & - 1 & - 5 \\5 & 1 & 4 & 5\end{array} \right]$

Solve using Cramer's Rule. -Jerry has 3 pieces of string. The total length is 102 inches. The sum of the two longer pieces is 83. The middle piece is twice as long as the shortest piece. What are the lengths of the 3 pieces?