Question
Fene aigomvalues for Ina system:Satone orote:D6z 0 0 $ Dd 3
Fene aigomvalues for Ina system: Satone orote: D6z 0 0 $ Dd 3
Answers
Solve each system of equations. $$\begin{aligned}&3 c_{1}+3 c_{2}=0\\&2 c_{1}+3 c_{2}=0\end{aligned}$$
So this is problem 16 Section 7.6 and were asked to solve this system by Gaussian elimination. And the first thing you actually notice is that I'm a bottom here. We have 00 zero. And what this equates to is, uh, X is equal to zero. And why has to be equal to zero for this system of equations? And if you notice it's actually inconsistent with this equation up here, which is, uh, ex is equal to three. And so because of this, our system is inconsistent and it has no solution.
So for this problem, we must solve the system by Gaussian elimination. So in order to do that, we have to recognize what each matrix or what each row in the Matrix is basically telling us. Well, this first row is saying that one X plus zero y is equal to three. We simplify that down to just X equals three. The second row is saying that zero x zero y is equal to zero. But we can write that zero. Why is equal to zero? Because that is true. You know, no matter what, the why is because we already have an axe here. So we're going to leave this a zero y equals zero. So what does the system of equations equations tell us? Well, it's saying that no matter what, why is why could be any number? It's always going to get multiplied by zero and be equal to zero, So it's going to be a solution. So what this problem is saying is that for anyone, for anyone, three is a solution. Why is that? Because three X is always going to be equal to three as long as why is any variable as well so we can make the inference that three why is going to be his solution for any wine, given this system of equations.
So here we have a specific chemical reaction where we have to a G I plus 10 E S S N two plus plus to a G plus to i minus. And we're given that not sell Is equivalent to negative 0.015V. So in order to find the equilibrium constant with respect to concentration, we have to relate uh the equilibrium constant and not sell through free energy. And by rearranging these equations, we can find that Casey is equivalent to E to the power of n F E over our tea. And we can find our equilibrium constant by substituting all our information into our equation here. And the first thing to see is that we need the number of moles of electrons transferred. So we have one reaction where this is occurring. We have the oxidation of 10 with two moles of electrons transfer. Since this is a balanced chemical reaction, the other must accept essentially two electrons. So we have two moles of electrons transfer, been told And we're going to assume that this is occurring a temperature of 298 Calvin. Yeah. And we can substitute all our information into here. And as a result of this, We can find that our general equilibrium constant with respect to concentration is equivalent to 0.31 and this is our final answer.