Why is this matrix undefined?

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In summary, the conversation involves the discussion of two matrices, D and E, and their product DE. It is pointed out that the product of two matrices can be defined as the dot product of vectors consisting of the rows and columns of the matrices. It is also mentioned that while DE is defined, ED is not due to the difference in the number of components in each row and column. The conversation then shifts to the importance of actually doing the problems rather than just skimming through the material.
  • #1
1,755
1
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 ?
 
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  • #2
Oh crap, ignore me ... LOL, I'm thinking inner product rules ... :p
 
  • #3
? 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.
 
  • #4
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.
 
  • #5
rocomath said:
I'm not actually doing the problem, just skimming through the section.
Perhaps less skimming and more 'doing' is in order! :wink:
 
  • #6
cristo said:
Perhaps less skimming and more 'doing' is in order! :wink:
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 :)
 

1. Why is this matrix undefined?

A matrix is undefined when it does not have a defined value. This can happen for several reasons, such as having a zero determinant, being non-square, or having a division by zero.

2. How can I tell if a matrix is undefined?

You can tell if a matrix is undefined by checking its properties, such as its dimensions and determinant. If the matrix is non-square or has a determinant of zero, it is considered undefined.

3. Can I perform operations on an undefined matrix?

No, you cannot perform operations on an undefined matrix. This is because it does not have a defined value, so any calculations would be meaningless.

4. What does it mean if a matrix is singular?

If a matrix is singular, it means that it is undefined. This is because a singular matrix has a determinant of zero, which means it does not have a unique solution.

5. How can I avoid getting an undefined matrix?

To avoid getting an undefined matrix, you should ensure that the matrix has a non-zero determinant and is square. You should also avoid dividing by zero when performing operations on a matrix.

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