# How do you solve x+y-z=-2, 2x-y+z=5, and -x+2y+2z=1 using matrices?

##### 1 Answer
Apr 28, 2016

(x,y,z) = (1,-1,2)

#### Explanation:

First, we can observe the fact that each one of these equations represents a plane in ${R}^{3}$

Additionally, since each equation is nonhomogeneous (as is the system), each of the three planes will be translated off of the origin.

Finally, it can be noted that this system may be described as "consistent and independent" (the dimension of the column space = the dimension of the row space = 3).