# System of 5 equations

1. Aug 28, 2015

### DanielSauza

Hello, I've come across the following system during my finite element theory class. I'm not quite sure about how to figure out the values of u3, u4, u5, R1 and R2. I've heard something about using Jordan's matrix properties but I'm not familiar with those. How would you go about solving this system?

Sorry for my english, not my first language.

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2. Aug 29, 2015

### Simon Bridge

How would you normally go about solving such systems?

3. Aug 30, 2015

### HallsofIvy

Staff Emeritus
It is very hard to read what you have there! It appears to be
$$\begin{bmatrix}R_1 \\ R_2 \\ 10 \\ 0 \\ 10 \end{bmatrix}= \begin{bmatrix}8 & 0 & -5 & 0 & 0 \\ 0 & 10 & 0 & 0 & -10 \\ -5 & 0 & 18 & 7 & -20 \\ 0 & 0 & -8 & 23 & -10 \\ 0 & -10 & -20 & -10 & 40 \end{bmatrix} \begin{bmatrix}0 \\ 0 \\ u_3 \\ u_4 \\ u_5\end{bmatrix}$$

Is that correct? And is the right side a matrix multiplication? If so then the 5 equations are
$-5u_3= R_1$
$-10u_5= R_2$
$18u_3+ 7u_4- 20u_5= 10$
$-8u_3+ 23u_4- 10u_5= 0$ and
$-20u_3- 10 u_4+ 40u_5= 0$.

The first thing I notice is that the last three equation involve $u_3$, $u_4$, and $u_5$ without any $R_1$ or $R_3$ so can be solved as "three equations in three unknowns". Then $R_1$ and $R_2$ can be calculated from the first two equations.