91Ó°ÊÓ

Determine whether each of the following statements is true or false: Gauss-Jordan elimination produces a matrix in reduced row-echelon form.

Determine whether each of the following statements is true or false: An inconsistent system of linear equations has infinitely many solutions.

Apply a graphing utility to perform the indicated matrix operations, if possible. $$A=\left[\begin{array}{rrrr}1 & 7 & 9 & 2 \\\\-3 & -6 & 15 & 11 \\\0 & 3 & 2 & 5 \\\9 & 8 & -4 & 1\end{array}\right] \quad B=\left[\begin{array}{rr}7 & 9 \\\8 & 6 \\\\-4 & -2 \\\3 & 1\end{array}\right]$$ $$A A$$

Determine whether each of the following statements is true or false: Every system of linear equations with a unique solution is represented by an augmented matrix of order \(n \times(n+1)\) (Assume no two rows are identical.)

A copy machine accepts nickels, dimes, and quarters. After one hour, it holds 30 coins total, and their value is \(\$ 4.60\) How many nickels, quarters, and dimes are in the machine?

Apply a graphing utility to perform the indicated matrix operations, if possible. $$A=\left[\begin{array}{rrrr}1 & 7 & 9 & 2 \\\\-3 & -6 & 15 & 11 \\\0 & 3 & 2 & 5 \\\9 & 8 & -4 & 1\end{array}\right] \quad B=\left[\begin{array}{rr}7 & 9 \\\8 & 6 \\\\-4 & -2 \\\3 & 1\end{array}\right]$$ $$A^{5}$$

Apply a graphing utility to perform the indicated matrix operations. $$A=\left[\begin{array}{rrrr}1 & 7 & 9 & 2 \\\\-3 & -6 & 15 & 11 \\\0 & 3 & 2 & 5 \\\9 & 8 & -4 & 1\end{array}\right]$$ Find \(A^{-1}\)

Solve the system of equations. $$ \begin{array}{l} \frac{3}{x}-\frac{4}{y}+\frac{6}{z}=1 \\ \frac{9}{x}+\frac{8}{y}-\frac{12}{z}=3 \\ \frac{9}{x}-\frac{4}{y}+\frac{12}{z}=4 \end{array} $$

Apply a graphing utility to perform the indicated matrix operations. $$A=\left[\begin{array}{rrrr}1 & 7 & 9 & 2 \\\\-3 & -6 & 15 & 11 \\\0 & 3 & 2 & 5 \\\9 & 8 & -4 & 1\end{array}\right]$$ Find \(A A^{-1}\)

The sides of a triangle are formed by the lines \(x-y=-3,3 x+4 y=5,\) and \(6 x+y=17 .\) Find the vertices of the triangle.