- #1
Chacabucogod
- 56
- 0
I was reading the finite element method in engineering by Rao and in the first example he ends up with a matrix that is singular.
The matrix is the following:
[tex]
\begin{pmatrix}
2 &-2 & 0\\
-2 & 3&-1\\
0&-1& 1
\end{pmatrix}
[/tex]
Which is a symmetric matrix as far as I can remember. Now you have 3 Nodes that will be the vector that will multiply this matrix the first node you already know is zero
so:
[tex]
\begin{pmatrix}
0\\
f1\\
f2
\end{pmatrix}
[/tex]
The solution vector is
[tex]
\begin{pmatrix}
P1\\
0\\
1
\end{pmatrix}
[/tex]
Now he says that you can eliminate row 1 and column 1, but if you multiply the matrix by the first element of the vector only column one disappears. I tried solving this with the transpose method, but it seems there's no way to solve this matrix. Since there are only 2 unknowns can I completely forget ably the 3*3 matrix and do a 2*2 or do I have to take into account the third equation (the one that comes out of row 1)
Thank you
The matrix is the following:
[tex]
\begin{pmatrix}
2 &-2 & 0\\
-2 & 3&-1\\
0&-1& 1
\end{pmatrix}
[/tex]
Which is a symmetric matrix as far as I can remember. Now you have 3 Nodes that will be the vector that will multiply this matrix the first node you already know is zero
so:
[tex]
\begin{pmatrix}
0\\
f1\\
f2
\end{pmatrix}
[/tex]
The solution vector is
[tex]
\begin{pmatrix}
P1\\
0\\
1
\end{pmatrix}
[/tex]
Now he says that you can eliminate row 1 and column 1, but if you multiply the matrix by the first element of the vector only column one disappears. I tried solving this with the transpose method, but it seems there's no way to solve this matrix. Since there are only 2 unknowns can I completely forget ably the 3*3 matrix and do a 2*2 or do I have to take into account the third equation (the one that comes out of row 1)
Thank you