Question

If A is a 3x3 matrix for which the row echelon form has 2 leadings 1s,

would this be an accurate depiction of what they are describing?

http://i.imgur.com/3dZH9We.png

or does d = 0 for it to be in row echelon form?

Answer 1

I guess I could answer my own question based on the rank rules

Answer 2

echelon is a word that means stairs, or steps ...

a reduced row echelon form is when its stepped AND has leading 1s in each row. if the bottom row is all zeros, then it has reduced to an equivalent dependant matrix

Answer 3

wait probably not

Answer 4

at the moment, your setup is in a stepped row fashion with 2 leading 1s

Answer 5

1 3 2
0 2 -1
0 0 5

this is a row echelon, a stepped row, form. with 1,2,5 as the leading values

Answer 6

The question I'm answering asks me if this matrix, Ax=b has infinitely many solution for any b.

I put false because,

if d =/= 0, the system is inconsistent

Answer 7

and thus there are no solutions for b

Answer 8

or I could just say q < p therefore no solutions

where q and p are rank of coefficient and augmented respectably

Answer 9

http://stattrek.com/matrix-algebra/echelon-form.aspx

there are 2 competing ideas ... stattrek presents ref, as leading 1s; but notes, "Some references present a slightly different description of the row echelon form. They do not require that the first non-zero entry in each row is equal to 1."

Answer 10

So this is kind of up in the air?

Answer 11

its up to your specific material :)

Answer 12

I have no clue what my prof wants lol

Answer 13

and I'm using the old text book for the course so yeah.

Answer 14

when theres a difference of opinions, then you simply have to go with your materials opinion :) ask your prof or see if your material defines it better.

Answer 15

thank you for the help amistre64 I will just answer it both ways.

Answer 16

I'm pretty sure your way is the way we are handling it, I will ask my TA

Answer 17

no as for inconsistent ... 0=0 is always true, which would indicate a dependant set of vectors.

1 3 | 4
2 6 | 8

this system reduces to

1 3 | 4
0 0 | 0

as it should since the system is describing concurrent lines .... the same line in 2 different ways .. 0=0 always



whereas:

1 3 | 4
2 6 | -4

reduces to

1 3 | 4
0 0 | -8

this represents parallel lines .... 2 different lines that never touch and therefore an inconsistency develops ... no solution is possible becuase 0 = -8 never

Answer 18

typo at the start :/

*now as for inconsistent ...

Answer 19

and -12 .. but my minds frail lol

Answer 20

:) well I appreciate all your help thank you so much.

Answer 21

if we assumed d = 0 though the system would only have 1 solution right by q = p = n

Answer 22

if d=0 that simply means that one of the column vectors is useless in defining the most efficient number of vectors to define the system with. it means that at least one of the vectors is a linear combination of the others.

Answer 23

solutions tho would be attributed to an augmented matrix such that the last column defines the equality of the system