91Ó°ÊÓ

Use an inverse matrix to solve (if possible) the system of linear equations. $$\left\\{\begin{array}{l}18 x+12 y=13 \\\30 x+24 y=23\end{array}\right.$$

Write a cryptogram for the message using the matrix \(A=\left[\begin{array}{rrr} 1 & 2 & 2 \\ 3 & 7 & 9 \\ -1 & -4 & -7 \end{array}\right]\). OPERATION OVERLOAD

Use the matrix capabilities of a graphing utility to evaluate the determinant. $$\left|\begin{array}{rrrr} 0 & -3 & 8 & 2 \\ 8 & 1 & -1 & 6 \\ -4 & 6 & 0 & 9 \\ -7 & 0 & 0 & 14 \end{array}\right|$$

Use determinants to find the area of a triangle with vertices \((3,-1),(7,-1),\) and (7,5) Confirm your answer by plotting the points in a coordinate plane and using the formula Area \(=\frac{1}{2}(\text { base })(\text { height })\).

Evaluate the determinant(s) to verify the equation. $$\left|\begin{array}{ll} w & x \\ y & z \end{array}\right|=\left|\begin{array}{ll} w & x+c w \\ y & z+c y \end{array}\right|$$

Find square matrices \(A\) and \(B\) to demonstrate that \(|A+B| \neq|A|+|B|\).

A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The tape was paused three times, and the position of the ball was measured each time. The coordinates obtained are shown in the table. \((x \text { and } y\) are measured in feet.) $$\begin{array}{|l|c|c|c|} \hline \text { Horizontal Distance, } x & 0 & 15 & 30 \\ \hline \text { Height, } y & 5.0 & 9.6 & 12.4 \\ \hline \end{array}$$ (a) Use a system of equations to find the equation of the parabola \(y=a x^{2}+b x+c\) that passes through the three points. Solve the system using matrices. (b) Use a graphing utility to graph the parabola. (c) Graphically approximate the maximum height of the ball and the point at which the ball struck the ground. (d) Analytically find the maximum height of the ball and the point at which the ball struck the ground. (e) Compare your results from parts (c) and (d).