Hey bugatti79.
Can you reduce it to reduced row-echelon form to show what is linearly dependent?
I am trying to establish what interpolation functions he used to obtain the 8 approximation functions (eqn 5.3.25a) shown in the attached excerpt from the book.
He states that a cubic approximation can be used for and an interpendent quadratic approximation for thus I write
Putting into matrix form and inverting to find the c values wolfram comes up with the matrix being singular (note I am using dummy variables).
inverse[{{1,x,x^2,x^3},{1,x,x^2,0},{1,y,y^2,y^3},{1,y,y^2, 0}}] - Wolfram|Alpha
Note: This has been submitted to PF 3 weeks ago with no response
Interdependent Interpolation Element- Timoshenko Beam
Regards
bugatti
Hi Chiro,
See link from Wolfram [{{1,x,x^2,x^3},{1,x,x^2,0},{1,y,y^2,y^3},{1,y,y^2, 0}}] row echelon form - Wolfram|Alpha
This indicates the functions are linearly dependent, right?
Yeah it's definitely linear dependent because the last row in the last column has a 0.
The next step is to figure out exactly what other vectors the last is linearly dependent on: in other words write {1,y,y^2,0} in terms of a linear combination of the other basis vectors and this will highlight what other data it depends on.
For the second question you need to consider how to write {1,y,y^2,0} = a*{1,x,x^2,x^3} + b*{1,x,x^2,0} + c*{1,y,y^2,y^3} for constants a, b, and c.
For the first question you might want to calculate the symbolic determinant such that it is unequal to zero for a given value of a_24 and a_44 and see what values they have to be to get a proper inverse.