Why they stack the vector that way

  • Thread starter transgalactic
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    Vector
In summary, the conversation discusses the use of row and column reduction in finding the dimension of a sum of vectors. It is mentioned that flipping the vectors and using a row reduction can lead to different results compared to using the original vectors and performing a column reduction. However, it is stated that both methods are equally valid in solving the problem.
  • #1
transgalactic
1,395
0
v1 is
(0)
(1)
(2)
(3)

v2 is
(2)
(a)
(1)
(0)

W1 is
(3)
(1)
(1)
(0)

W2 is
(-2)
(4)
(2)
(6)

i am asked to find the dim of v+w ??

i was told to flip each vector by 90 degrees
so
(a)
(b)
(c)
(d)

in the matrix presented a a row (a b c d)
and then do a row reduction

but they just keep it as it they were originaly (as columns) and do a row reduction

0 2 3 -2
1 a 1 4
2 1 1 2
3 0 0 6


??
 
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  • #2
Hi transgalactic! :wink:

I'm not sure what your question is,

but if you're asking whether using a column reduction is just as valid as using a row reduction, the answer is yes. :smile:
 
  • #3
no they present them as columns instead of flipping them
and then they do a row reduction

??
 
  • #4
He answered your question: it doesn't matter whether you represent vectors as columns or rows!
 
  • #5
ahhh ok
thanks :)
 
  • #6
it does matter
because when i flipped it and did a row reduction i got
-2 4 2 6
0 10 8 6
0 0 -2-8a -6a+36
0 0 0 10a+40

but in the not flipped version i get
1 0 0 -2
0 1 0 4
0 0 1 2
0 0 0 -3a -3

??
 

1. Why is the vector stacked in a specific order?

The specific order of a vector is determined by its purpose and the data it contains. For example, if a vector represents the coordinates of points in a graph, it may be stacked in a particular order to make plotting easier. If a vector contains data on different categories, it may be stacked in alphabetical or numerical order.

2. Is there a standard way to stack a vector?

There is no standard way to stack a vector as it depends on the context and purpose of the data. However, there are some common conventions, such as stacking in ascending or descending order, or separating data into categories.

3. Can the order of a stacked vector be changed?

Yes, the order of a stacked vector can be changed. This can be done manually by rearranging the data or using functions in a programming language to manipulate the vector. However, changing the order of a stacked vector may affect the interpretation and analysis of the data.

4. How does the stacking order affect data analysis?

The stacking order of a vector can affect data analysis in different ways. For example, if the vector is stacked in ascending order, it may be easier to identify trends or patterns in the data. Additionally, changing the order of a stacked vector may result in different insights and conclusions from the data.

5. Are there any benefits to stacking a vector in a specific way?

Yes, there can be benefits to stacking a vector in a specific way. For instance, stacking data in a logical or meaningful order can make it easier to understand and interpret. It can also make it easier to perform calculations or operations on the data, especially in programming languages.

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