Question

o TP & E Write the augmented matrix of the system and use it to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter z. X = y = Z= - 3x + - 2x + y 4y 4y + - 2z = -8 7z = 26 8z = 30 Question Help: Video 1 Video 2 M Message instructor​

Answer 1

The system of equations can be written as a matrix and then used to solve for the variables x, y, and z.

The augmented matrix of the system is:

-3 -2 1 | -8

0 4 -2 | -8

0 0 7 | 26

We can use row operations to find the row reduced echelon form of the matrix, which will give us the solutions to the system.

Starting with the first row:

1. Multiply row 1 by -3 to get a leading 1 in the first column:

3 6 -3 | 24

0 4 -2 | -8

0 0 7 | 26

2. Add row 1 to row 2:

3 6 -3 | 24

0 4 0 | 16

0 0 7 | 26

3. Add 3 times row 1 to row 3:

3 6 -3 | 24

0 4 0 | 16

0 0 7 | 26

The row reduced echelon form of the matrix is:

1 2 -1 | 8

0 1 0 | 4

0 0 1 | 9

From this, we can see that the solutions to the system are:

x = 8 - 2y

y = 4

z = 9

So the system has a unique solution: x = 8 - 2y = 8 - 2 * 4 = 0, y = 4, z = 9.