Why is matrix multiplication undefined for D and E?

[rocomath]

3D + E

D = 2 x 3

-1 2 3
4 0 5

E = 3 x 2

2 1
8 -1
6 5

D has 3 columns, and E has 3 rows ?

 

[rocomath]

Oh crap, ignore me ... LOL, I'm thinking inner product rules ... :p

 

[HallsofIvy]

? What matrix are you talking about? You give two matrices, D and E, both of which are defined because you just defined them.

The product DE is also defined but ED is not. Is that what you are talking about? Do I get a prize for guessing that?

The product of of two matrices, A and B can be defined as "the ij-component is the dot product of vectors consisting of the ith row of A and the jth column of B".

ED is not defined because each row of E has 2 components while each column of D has 3 components. You cannot take the dot product of two such vectors.

As you point out, the number of columns of D and the number of rows of E are the same- that is why DE is defined.

 

[rocomath]

Sorry Ivy! I misread the problem and kept thinking I was multiplying the two, the problem actually asks the addition of the two. I'm not actually doing the problem, just skimming through the section.

 

[cristo]

I'm not actually doing the problem, just skimming through the section.

Perhaps less skimming and more 'doing' is in order!

 

[rocomath]

Perhaps less skimming and more 'doing' is in order!

LOL, I know I should be doing the problems :( But, I did the examples and looked over the rules. I plan on doing a a good review after finals :)