building Matrix "echelon form"

Question

given is A = $ \begin{pmatrix} a & b & 0 & b \\ b & a & b & 0 \\ 0 & b & a & b \\ b & 0 & b & a \end{pmatrix} $

I need the echelon form for this matrix:

Whenever I begin calculating, I end up with an entry like "a/b", which isn't defined for b = 0. However, I am supposed to name the echelon form for real numbers a, b.

What am I doing wrong?

Do it by cases. If $b=0$, then the echelon form will be whatever it will be. If $b\neq 0$, then it's whatever you got. — Git Gud, Oct 19 '13 at 15:07

score 1 · Accepted Answer · answered Oct 19 '13 at 15:10

1

First switch the last row with 3rd row

Then divide your first Row by a to introduce a leading 1 then all you need to do is perform operations to make all elements below the leading 1 ZERO .

e.g after doing 1st step perform $$ R_2 - bR_1 $$ then perform $$ R_3 - bR_1 $$

Repeat this with remaining rows

answered Oct 19 '13 at 15:10

Taimoor Ali

76

and yea you have to assume the denominator variable to be non zero if any appears... – Taimoor Ali Oct 19 '13 at 15:14
I'am eager to ask do you notice the symmetry : the main diagonal is same and the corresponding elements above and below the diagonal are the same – Taimoor Ali Oct 19 '13 at 15:18
Hi! Thank you very much. I noticed the symmetry, but I didn't know what to do with this knowledge :D – Vazrael Oct 19 '13 at 16:51
If i helped you can give my answer a like up :) – Taimoor Ali Oct 19 '13 at 18:37
This might be of relevance to you http://math.stackexchange.com/questions/12220/symmetrize-eigenvectors-of-degenerate-repeated-eigenvalue – Taimoor Ali Oct 19 '13 at 18:43
@KevinLiebing kmkmkmkmkmkmkmkmkmk – Taimoor Ali Oct 19 '13 at 23:01
Hi, I already did :) In the end I get the following matrix, is this correct? $\begin{vmatrix} a & b & 0 & b \ 0 & b & a & b \ 0 & 0 & 2ab-\frac{a^3}{b} & -a^2 \ 0 & 0 & 0 & a^2 \end{vmatrix} $ – Vazrael Oct 20 '13 at 08:47

building Matrix "echelon form"

1 Answers1