Question

Is this set of vectors impossible to row reduce?

[6 4 -2 4], [2 0 0 1], [3 2 -1 2], [5 6 -3 2], [0 4 -2 -1]

I can't seem to row reduce it.. so I'm assuming it's not possible?

Answer 1

\[\left[\begin{matrix}2 & 1 &1&3&1 \\ 2 &0 &1&3&2\\ -2&0&-1&-3&-2\\2&1&1&-1&-3\end{matrix}\right]\]

This is what I got to so far by first subtracting row1 by row4. And then I added row2 and row3. Finally, I added row3 and row4.

Answer 2

row reducing is just using elementary row operations to reduce things down to 1s and 0s; or something cclose to it

Answer 3

are those your column vectors?

Answer 4

The vectors in the questions are I think row vectors since it stated that it was R2(1x2 matrices)

Answer 5

Yes, I did use the elementary row operations but I ended up having the "first" leading 1 in the fourth row instead of the first row.

Answer 6

you can move rows up and down as needed

Answer 7

the system:

2x + 3y = 4
x - 2y = 2

has the same solutions as:

x - 2y = 2
2x + 3y = 4

Answer 8

im still not sure how your post gets setup tho

Answer 9

Oh, I forgot about how you can interchange the rows. Thanks a lot amistre!

Answer 10

youre welcome