91Ó°ÊÓ

In Problems 35-42, each matrix is the reduced echelon matrix for a system with variables \(x_{1}, x_{2}, x_{3}\), and \(x_{4}\). Find the solution set of each system. \(\left[\begin{array}{rrrr:r}1 & 3 & 0 & 0 & 9 \\ 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 1 & -3 \\ 0 & 0 & 0 & 0 & 0\end{array}\right]\)

Solve each system by using the substitution method. \(\left(\begin{array}{c}\frac{2 x}{3}-\frac{y}{2}=\frac{3}{5} \\\ \frac{x}{4}+\frac{y}{2}=\frac{7}{80}\end{array}\right)\)

In Problems 35-42, each matrix is the reduced echelon matrix for a system with variables \(x_{1}, x_{2}, x_{3}\), and \(x_{4}\). Find the solution set of each system. \(\left[\begin{array}{rrrr:r}1 & 0 & 0 & 0 & 7 \\ 0 & 1 & 0 & 0 & -3 \\ 0 & 0 & 1 & -2 & 5 \\ 0 & 0 & 0 & 0 & 0\end{array}\right]\)

What is a matrix? What is an augmented matrix of a system of linear equations?

Explain the difference between a matrix and a determinant.

Solve each system by using the substitution method. \(\left(\begin{array}{rl}\frac{2}{3} x+\frac{1}{2} y & =\frac{1}{6} \\ 4 x+6 y & =-1\end{array}\right)\)

Solve each system by using the substitution method. \(\left(\begin{array}{rl}\frac{1}{2} x+\frac{2}{3} y & =-\frac{3}{10} \\ 5 x+4 y & =-1\end{array}\right)\)

Explain the concept of a cofactor and how it is used to help expand a determinant.

Describe how to use matrices to solve the system $$ \left(\begin{array}{r} x-2 y=5 \\ 2 x+7 y=9 \end{array}\right) \text {. } $$

What does it mean to say that any row or column can be used to expand a determinant?