Data Analysis The table shows the numbers $y$ (in millions) of motor vehicle registrations in the United States for the years $1997$ through $1999.$

$$\begin{array}{|c|c|} \hline \text{Year},t & \text{Registration},y\\ \hline 1997 & 207.8 \\ 1998 & 211.6 \\ 1999 & 216.3 \\ \hline \end{array}$$

Use the result of the previous Exercise to estimate when the number of vehicle registrations will reach $240$ million.

use the matrix capabilities of a graphing utility to write the augmented matrix corresponding to the system of equations in reduced row-echelon form. Then solve the system. {2x + 10y + 2z = 6 , x + 5y + 2z = 6 , x + 5y + z = 3 , -3x - 15y - 3z = -9

Met matrices A, B, C, and D be of orders , and , respectively. Determine whether the matrices are of proper order to perform the operation(s). If so, give the order of the answer. BC

find the inverse of the matrix (if it exists). [0 -2 1 , -5 -2 -3 , 7 3 4]

evaluate the determinant(s) to verify the equation. |w x , cw cx| = 0

Met matrices A, B, C, and D be of orders , and , respectively. Determine whether the matrices are of proper order to perform the operation(s). If so, give the order of the answer. AB

In this exercise, use Gauss-Jordan elimination to find the inverse of the matrix (if it exists).

$$\left[\begin{array}{rrr}-1 & -2 & -2 \\ 3 & 7 & 9 \\ 1 & 4 & 7\end{array}\right]$$

evaluate the determinant(s) to verify the equation. |w x , y z| = |w x+ cw , y z + cy|

use the matrix capabilities of a graphing utility to write the augmented matrix corresponding to the system of equations in reduced row-echelon form. Then solve the system. [ 3x + 3y + 12z = 6 , x + y + 4z = 2 , 2x + 5y + 20z = 10, -x + 2y + 8z = 4

evaluate the determinant(s) to verify the equation. |w cx , y cz| = c |w x , y z|

use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution. [ x + 2y = 0 , x + y = 6 , 3x - 2y = 8

find the inverse of the matrix (if it exists). [-3 -5 , 2 3]

Met matrices A, B, C, and D be of orders , and , respectively. Determine whether the matrices are of proper order to perform the operation(s). If so, give the order of the answer. B-3C

Find a singular 2 x 2 matrix satisfying A^2 = A