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Matrix Operations - Problem 1

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Adding matrices. Whenever we add matrices there is one key thing that we always have to check for first and that is making sure that our matrices have the same dimension. In order to add matrices they have to have the same dimension.

Looking at our three matrices we have on the board. Remember that the dimensions are the number of rows by the number of columns so this matrix is a 2 rows by 3 columns this one is 2 by 3 as well and this one here we have 3 rows and 2 columns.

So if I ask you to add A plus B we have right here, what this is saying is add matrix A plus matrix B each letter is just representing that matrice. The first thing we have to do is check to see that they have the same dimension. We just figure that out they are both 2 by 3 so we are good okay. So we are just going to rewrite this and work through our big plus sign in the middle and we can figure out where we go from here. 3 -2 4, 0 1 2, okay when adding matrices all you have to do is add the element that is in the same spot in each matrice.

So what we are going to do is we are going to add this together and we are going to end up with the same exact dimension, so we are going to have a 2 by 3 matrix. And how we find this part is just by adding the same corresponding elements. So the first part is going to be this 0 plus this 3.

So 0 plus 3 that’s going to go in this first part as well which will be A3. Going over the second spot we take this second element here and the second element here and we add them together, 1 plus -2 -1. And we do this going through the entire matrice. So 4 plus 4 is 8, 4 plus 0 is 4, -2 plus 1, -1, 7 plus 2 is 9. So by adding the corresponding elements in each matrix we end up getting this sum.

Subtraction is exactly the same instead of adding them you take the difference. What if we are asked to do another sum let’s say we are doing A plus C this time okay remember the first thing we have to do is make sure they are the same dimension we found that matrix A is 2 by 3 matrix C is 3 by 2. Those dimensions are different so we actually can’t add this. So this is impossible, there is no way to do that.

So whenever you are adding matrices make sure you have the same dimension and then add the corresponding parts, subtraction is exactly the same as well.

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