Question

he matrix below represents a system of equations.

2 1 1 4
-3 2 -1 -8
1 -1 1 5

Which matrix represents the solution to this system of equations?
mc024-2.jpg
mc024-3.jpg
mc024-4.jpg
mc024-5.jpg

Answer 1

The solution is x = 1, y = −1, z = 3. So the solution matrix (column vector) is

[1
-1
3]

Quick work: from the first and third equations subtract to get x + 2y = −1. Adding the first and second gives −x + 3y = −4, so x = 3y + 4. Substitute into x + 2y = −1 to get y = −1, then x = 1 and z = 3 (from x − y + z = 5).