( 1 0 0 2
1 1 0 2
2 0 1 4) please put in reduced row echelon form

Question

( 1 0 0 2
  1 1 0 2
  2 0 1 4) please put in reduced row echelon form

zarkon · Answer

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

amistre64 · Answer

http://www.wolframalpha.com/input/?i=rref+%7B1%2C0%2C0%2C2%7D%2C%7B1%2C1%2C0%2C2%7D%2C%7B2%2C0%2C1%2C4%7D

amistre64 · Answer

yeah, what zarkon did ;)

anonymous · Answer

so im not crazy i got this same answer but doesnt all off diagonals have to be zero

zarkon · Answer

no...only when there is a leading one in that particular column

anonymous · Answer

please tell me how you find column rank of a rectangular matrices

zarkon · Answer

how many leading ones do you have

anonymous · Answer

i mean if any of my above columns are linearly dependent..the original question

anonymous · Answer

3 leading 1s it is a 3x4

zarkon · Answer

so for this matrix the column rank is 3

zarkon · Answer

The column rank of a matrix A is the maximum number of linearly independent column vectors of A.  you have 3 in this case.

anonymous · Answer

even though it is not a square matrix?

zarkon · Answer

again ...  by definition ...
"The column rank of a matrix A is the maximum number of linearly independent column vectors of A."  

A can be any size.

anonymous · Answer

and it is linearly independent if there is no full column of zeros right?

zarkon · Answer

the first 3 column vectors of your matrix are L.I. since when you row reduced you got leading ones in those columns

zarkon · Answer

there is no leading one in the 4th column...therefore it can be written as a linear combination of the first 3 column vectors

anonymous · Answer

ohhhhhhh so the 4th column would be the linearly dependent one?

zarkon · Answer

notice 2 times the first column is equal to the 4th column

anonymous · Answer

yes sir and thts what makes it dependent ok