Answers
If a matrix is NOT a square matrix, are the row or column vectors linearly dependent? How do we show that?
I love this movie so I just had to post the trailer to represent.
i have gone into the text settings but cannot find anything that will let me change my text tone.
this is not a question this is a statement. the matrix is a possibilty and i have not been "watching to many movies" i believe that the idea of the matrix is a reality, what do you think?
You know. I'm fascinated. Please email me and tell me what and why you think this. What evidence do you have?
And Neo, watch out for that Cipher...
Anyway, I suppose anything is possible, and it makes sense for truly scientific minds to consider any possiblity. Although what we could do about it if it were is pretty limited.
What are the dimensions of the resulting matrix found by multiplying a 2 by 3 matrix and a 4 by 2 matrix?
2 by 2
3 by 4
2 by 4
this is not possible
thanks!
2×3 by 4×2
is not possible
Let A = n×m
Let B = m×p
A·B = n×p
The inner dimension must be the same.
The matrix A is
1 3
4 10
And i you can get reduced echelon form as follows:
1 3
4 10 R2: R2 - 4R1
which gives
1 3
0 -2 R2: -0.5R2
which gives
1 3
0 1
which is reduced echelon form. But how do you get the product of the matrix A from this?
Every time you do an elementary row operation, you are actually multiplying the original matrix by a corresponding elementary matrix!
To create an elementary matrix given the row operation, you just act on the appropriately sized identity matrix (in this case, 2 by 2) in the same way.
For your example, applying R2: R2 - 4R1 to
1 0 gives
0 1
1 0
-4 1.
This last matrix is the corresponding elem. matrix to your row operation. Call this E1
Likewise, applying R2: -0.5R2 to
1 0 gives
0 1
1 0
0 -.5
We'll call this E2.
So, your reduced echelon matrix should be equal to (E2)(E1)(A). Note the order of the elementary matrices is multiplied by A to its left in reverse order!
Double check (multiplying left to right):
1 0 * 1 0 * 1 3
0 -.5 * -4 1 * 4 10
equals
1 0 * 1 3
2 -.5 * 4 10
equals
1 3
0 1
as required!