I spent almost 2 days to solve the following stiffness matrix(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\left(\begin{array}{c}f1\\f2\\f3\\f4\\f5\end{arr ay}\right)=\left(\begin{array}{ccccc}20&-20&0&0&0\\-20&40&-20&0&0\\0&-20&40&-20&0\\0&0&-20&40&-20\\0&0&0&-20&20\end{array}\right)\left(\begin{array}{c}0\\d2\\d3\\d4\\0\end{arr ay}\right)?[/tex]

I have tried to partition the matrix like the following

FIRST

[tex]\left(\begin{array}{c}f1\\f2\\f3\end{array}\right)=\left(\begin{array}{ccc}20&-20&0\\-20&40&-20\\0&-20&40\end{array}\right)\left(\begin{array}{c}0\\d2\\d3\end{array}\right)+\left(\begin{array}{cc}0&0\\0&0\\-20&0\end{array}\right)\left(\begin{array}{c}d4\\0\end{array}\right)[/tex]

SECOND

[tex]\left(\begin{array}{c}f4\\f5\end{array}\right)=\left(\begin{array}{ccc}0&0&-20\\0&0&0\end{array}\right)\left(\begin{array}{c}0\\d2\\d3\end{array}\right)+\left(\begin{array}{cc}40&-20\\-20&20\end{array}\right)\left(\begin{array}{c}d4\\0\end{array}\right)[/tex]

but still cannot solve for the equation.

The partitioned matrix produced UNDETERMINED Multiplication and Addition of 2 matrices.

Can anyone help me on this, please...

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# Stiffness Matrix

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