91Ó°ÊÓ

Use Cramer's Rule to solve each system. $$\left\\{\begin{array}{l}2 x=3 y+2 \\\5 x=51-4 y\end{array}\right.$$

In Exercises \(29-32,\) write each linear system as a matrix equation in the form \(A X=B\), where \(A\) is the coefficient matrix and \(B\) is the constant matrix. $$\left\\{\begin{array}{l}x+3 y+4 z=-3 \\\x+2 y+3 z=-2 \\\x+4 y+3 z=-6\end{array}\right.$$

In Exercises \(37-44\), perform the indicated matrix operations given that \(A, B,\) and \(C\) are defined as follows If an operation is not defined, state the reason. $$A=\left[\begin{array}{rr}4 & 0 \\\\-3 & 5 \\\0 & 1\end{array}\right] \quad B=\left[\begin{array}{rr} 5 & 1 \\\\-2 & -2\end{array}\right] \quad C=\left[\begin{array}{rr}1 & -1 \\\\-1 & 1\end{array}\right]$$ $$B C+C B$$

Determinants are used to find the area of a triangle whose vertices are given by three points in a rectangular coordinate system. The area of a triangle with vertices \(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\) and \(\left(x_{3}, y_{3}\right)\) is $$\text { Area }-\pm \frac{1}{2}\left|\begin{array}{lll}x_{1} & y_{1} & 1 \\\x_{2} & y_{2} & 1 \\\x_{3} & y_{3} & 1\end{array}\right|$$ where the \(\pm\) symbol indicates that the appropriate sign should be chosen to yield a positive area. Use determinants to find the area of the triangle whose vertices are \((1,1),(-2,-3),\) and \((11,-3)\)