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Adding and Subtracting Matrices

If they aren't the same size, then you won't be able to match up the entries.

Check it out:

[ row 1: 1 , -3 row 2: 2 , 4 ] + [ row 1: 5 row 2: -6 ]
You can't do this!  Each guy MUST have a partner!
 

= [ row 1: 1 + 5 , -3 + ? row 2: 2 + ( -6 ) , 4 + ? ] ... the a11 guys are 1 and 5 ... the a21 guys are 2 and -6 ... the question marks show that there is nothing from the second matrix in entries a12 or a22
 

Hmm...  So, does this mean that we can add a 1 x 2 matrix and a 2 x 1 matrix?

Can we do it? [ 4 , -7 ] + [ row1: -3 row 2: 5 ]

No!  They are NOT the same size!  (And, no, you cannot just tip the second one on it's side, so stop thinking about it.)

TRY IT:

Add or subtract these, if possible:
 

[ row 1: -5 , 8 , -9 row 2: 7 , 0 , 12 ] + [ row 1: -3 , -4 , 0 row 2: 8 , 6 , -5 ]

 

[ row 1: 2 , 8 , 3 row 2: -6 , -2 , 4 ] + [ row 1: 8 , 0 row 2: -11 , 3 row 3: 12 , 5 ]

 

[ row 1: 3 , -6 row 2: 4 , -7 ] - [ row 1: 0 , -2 row 2: -4 , 6 ]