Question

Create a matrix for this linear system:

{
x
+
3
⁢
y
+
2
⁢
z
=
26
x
−
3
⁢
y
+
4
⁢
z
=
2
2
⁢
x
+
y
+
z
=
8

What is the solution of the system?

Answer 1

To create a matrix for this linear system, we can arrange the coefficients of the variables and the constants into a matrix as follows:

| 1 3 2 | | x | | 26 |

| 1 -3 4 | x | y | = | 2 |

| 2 1 1 | | z | | 8 |

To solve the system using row reduction, we can perform elementary row operations to transform the matrix into row echelon form or reduced row echelon form. I will use the latter approach for simplicity:

| 1 0 0 | | x | | 6 |

| 0 1 0 | x | y | = | 5 |

| 0 0 1 | | z | | -1 |

Therefore, the solution to the system is x = 6, y = 5, and z = -1.