91Ó°ÊÓ

Find an equation of the circle that passes through the points. $$(-5,1),(-3,2),(-1,1)$$

Find the solution set of the system of linear equations represented by the augmented matrix. $$ \left[\begin{array}{rrrr} 3 & -1 & 1 & 5 \\ 1 & 2 & 1 & 0 \\ 1 & 0 & 1 & 2 \end{array}\right] $$

Find the solution set of the system of linear equations represented by the augmented matrix. $$ \left[\begin{array}{llll} 1 & 2 & 0 & 1 \\ 0 & 1 & 2 & 1 \\ 0 & 0 & 1 & 2 & 1 \\ 0 & 0 & 0 & 1 & 4 \end{array}\right] $$

Graph the system of linear equations. Solve the system and interpret your answer. $$\begin{aligned}&2 x-y=5\\\&5 x-y=11\end{aligned}$$

The U.S. census lists the population of the United States as 249 million in \(1990,282\) million in \(2000,\) and 309 million in 2010 . Fit a second-degree polynomial passing through these three points and use it to predict the populations in 2020 and 2030 . (Source: U.S. Census Bureau)

Find the solution set of the system of linear equations represented by the augmented matrix. $$ \left[\begin{array}{ccccc} 1 & 2 & 0 & 1 & 3 \\ 0 & 1 & 3 & 0 & 1 \\ 0 & 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 0 & 2 \end{array}\right] $$

Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced rew-echelon form. $$ \left[\begin{array}{llll} 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 \end{array}\right] $$

Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced rew-echelon form. $$ \left[\begin{array}{llll} 0 & 1 & 0 \\ 1 & 0 & 2 & 1 \end{array}\right] $$

Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced rew-echelon form. $$ \left[\begin{array}{rrrr} -2 & 0 & 1 & 5 \\ 0 & -1 & 2 & 1 \\ 0 & 0 & 0 & 2 \end{array}\right] $$

Graph the system of linear equations. Solve the system and interpret your answer. $$\begin{aligned}&0.05 x-0.03 y=0.07\\\&0.07 x+0.02 y=0.16\end{aligned}$$