91Ó°ÊÓ

Both det(\(A\)) and |\(A\)| represent the ________ of the matrix \(A\).

For a square matrix, the entries \(a_{11}\), \(a_{22}\), \(a_{33}\), \(\ldots\), \(a_{nn}\) are the ________ ________ entries.

A message written according to a secret code is called a ________.

If a message is encoded using an invertible matrix \(A\), then the message can be decoded by multiplying the coded row matrices by ________ (on the right).

In Exercises 39-44, use a determinant to determine whether the points are collinear. \((0, 2)\), \((1, 2.4)\), \((-1, 1.6)\)

In Exercises 47-52, use a determinant to find an equation of the line passing through the points. \((0, 0)\), \((5, 3)\)

In Exercises 47-52, if possible, find (a) \(AB\), (b) \(BA\), and (c) \(A^2\). (Note: \(A^2 = AA\).) \(A=\left[\begin{array}{r} 3 & 2 & 1 \end{array}\right]\), \(B=\left[\begin{array}{r} 2 \\ 3 \\ 0 \end{array}\right]\)

PRODUCTION In Exercises 69-72, a small home business creates muffins, bones, and cookies for dogs. In addition to other ingredients, each muffin requires 2 units of beef, 3 units of chicken, and 2 units of liver. Each bone requires 1 unit of beef, 1 unit of chicken, and 1 unit of liver. Each cookie requires 2 units of beef, 1 unit of chicken, and 1.5 units of liver. Find the numbers of muffins, bones, and cookies that the company can create with the given amounts of ingredients. 700 units of beef 500 units of chicken 600 units of liver

TRUE OR FALSE? In Exercises 71-74, determine whether the statement is true or false. Justify your answer. In Cramer's Rule, the numerator is the determinant of the coefficient matrix.

LABOR/WAGE REQUIREMENTS A company that manufactures boats has the following labor-hour and wage requirements. \begin{equation} \stackrel{\mbox{\textrm{Labor per boat}}}{ \stackrel{\mbox{Department}}{ \overbrace{ \begin{array}{@{}r@{\quad}ccrr@{}} \textrm{Cutting} & \textrm{Assembly} & \textrm{Packaging} \\ \end{array}}}} \end{equation} \begin{equation} \left. S=\left[\begin{array}{@{}r@{\quad}ccrr@{}} 1.0h & 0.5h & 0.2h \\ 1.6h & 1.0h & 0.2h \\ 2.5h & 2.0h & 1.4h \end{array}\right] \begin{array}{r} \textrm{Small} \\ \textrm{Medium} \\\ \textrm{Large} \end{array}\right\\} \textrm{Boat size} \end{equation} Wages per hour \begin{equation} \stackrel{\mbox{Plant}}{ \overbrace{ \begin{array}{@{}r@{\quad}ccrr@{}} A & B \\ \end{array}}} \end{equation} \begin{equation} \left. T=\left[\begin{array}{@{}r@{\quad}ccrr@{}} \$15 & \$13 \\ \$12 & \$11 \\ \$11 & \$10 \end{array}\right] \begin{array}{r} \textrm{Cutting} \\ \textrm{Assembly} \\\ \textrm{Packaging} \end{array}\right\\} \textrm{Department} \end{equation} Compute \(ST\) and interpret the result.