How do you solve x+y-z=-2x+yz=2, 2x-y+z=52xy+z=5, and -x+2y+2z=1x+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 R3

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

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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).