Matrices question

  • #1
Karate Chop
18
0
when you're multiplying two matrices together does it affect the answer at all if you swap the columns around in one of the matrices?
 

Answers and Replies

  • #2
marlon
3,777
11
Karate Chop said:
when you're multiplying two matrices together does it affect the answer at all if you swap the columns around in one of the matrices?

yes it does, just look at the defnition of matrix multiplication :

[tex](AB)_{ij} = \Sigma_k a_{ik}b_{kj}[/tex]

try for yourself with an example

Here is some extra info : Matrix Multiplication
marlon
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
43,021
970
Did you consider doing a little experimentation?

What is [tex]\left( \begin{array}{ccc}1&2\\3&2\end{array}\right)\left(\begin{array}{ccc}2&-1\\2&1\end{array}\right)[/tex]?

Is that the same as [tex]\left( \begin{array}{ccc}1&2\\3&2\end{array}\right)\left(\begin{array}{ccc}-1&2\\1&2\end{array}\right)[/tex]?
 
  • #4
The Bob
1,119
0
Matrix multiplication is associative but not commutative.

E.g. A(BC) equals (AB)C but AB does not equal BA.

The Bob (2004 ©)
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
43,021
970
And that has what to do with the question?
 
  • #6
marlon
3,777
11
HallsofIvy said:
And that has what to do with the question?
:rofl: :rofl: :rofl: :rofl: :rofl:

answer : i dunno :rofl:
marlon
 
  • #7
primarygun
233
0
E.g. A(BC) equals (AB)C but AB does not equal BA.
Sometimes it does. Such as the square of a matrix.
 
  • #8
TD
Homework Helper
1,022
0
When we say matrix multiplication isn't commutative, we mean in general.
To be commutative it always has to be valid.

As you say though, there are exceptions (multiplying with the identy-matrix or with the inverse too for example) but that doesn't change the fact the multiplication isn't commutative.
 
  • #9
HallsofIvy
Science Advisor
Homework Helper
43,021
970
MY point was that the original question had to do with rearranging the columns in one of the matrices- giving a completely different matrix. It had nothing to do with the commutativity of multiplication.

Wandering off topic is just going to confuse the original poster.
 
  • #10
The Bob
1,119
0
HallsofIvy said:
And that has what to do with the question?
Apologises for misunderstanding the question. Glad to feel I can make mistakes and not have my gut knotted. :cry:

The Bob (2004 ©)
 

Suggested for: Matrices question

  • Last Post
Replies
4
Views
228
  • Last Post
Replies
2
Views
179
  • Last Post
Replies
8
Views
245
  • Last Post
Replies
11
Views
307
Replies
4
Views
177
  • Last Post
Replies
1
Views
222
  • Last Post
Replies
3
Views
178
  • Last Post
Replies
1
Views
240
  • Last Post
Replies
22
Views
349
Replies
13
Views
217
Top