(22, 5, -12 ) - (10, -5, 3 ) = ( 22 - 10, 5 - (-5), -12 - 3 ) = ( 12, 10, -15 )

(10, -5, 3 ) - (22, 5, -12 ) = ( 10 - 22, (-5) - 5, 3 - (-12) ) = (-12, -10, 15 ) 

Not Commutative

Another Math Fact emerges:

Matrix subtraction is NOT commutative.
This means that you can't change the order when doing a - b.

The negative of a matrix is this:

-a   means negate each element of   a.

So, for example:

-(22, 5, -12 ) = ( -22, -5, 12 )

-( 19.2, 28.6, 0.0 )T = ( -19.2, -28.6, 0.0 )T 

In symbols: if   a  is  ( a₀, a₁, ..., a₂)  then   -a   means ( -a₀, -a₁, ..., -a₂).

( -7.2, -98.6, 0.0 )T - ( -2.2, -2.4, 3.0 )T