Ok so thinking about this a bit more, I'm getting most of it. You say that since ##(1,0,0,0,0,0,0)\rightarrow(1,0)##
and also that ##(0,1,0,0,0,0,0)\rightarrow(1,0)##,
The 2D vectors are not perpendicular? I'm just struggling with the idea of why the 2D vectors in their 2D system aren't...
Can you elaborate a bit more? In a regular Ax=b formulation, where A is, say, a 3x3 matrix, the columns are vectors in 3D space. the elements of x are 'weighting factors' which multiply the columns (vectors) and the result b is the vector sum.
So we have
\begin{equation*}
\begin{pmatrix}
1 &...
It's from a linear programming question in standard form. It's a part of a worksheet we got, but I didn't want help with the whole question (so I didn't put it in the homework help forum), just understanding the meaning of the rectangular matrix. I've attached the question here for context.
By...
So if I have a system of equations:
$$x_1+x_2+x_3=1$$
and $$x_4+x_5+x_6=1$$
Then they can be put into a matrix representation
\begin{equation*}
\begin{bmatrix}
1 & 1 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 & 1 & 1\\
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
x_4 \\
x_5 \\
x_6 \\
\end{bmatrix}...
Thanks for the reply.I find that the commercially available buffer solutions have multiple constituents so calculating it's contribution to the conductivity (in order to subsequently be able to subtract it out) is not trivial.
So now I'm thinking of just adding NaOH or HCl, which dissociate...
Hi,
I need to conduct experiments at fixed pH. The complication is that the solution I'm using will have NaCl in it. So if I add HCl or NaOH to make the solution more acidic or basic, the conductivity of the solution (as measured by a conductivity meter) will change due to the added Na+ or Cl-...
Referring to first figure attached, if we put a system of a certain composition at a T and P corresponding to a point inside the spinodal, will it (with very small fluctuations) just jump to the corresponding binodal compositions at that temperature and pressure? As per this figure, the system...
Oh okay, I get your point. Thanks! Just to confirm with you, I had another problem where an elevator is falling through air and the Reynolds number is found to be much larger than 1,so that the flow is approximately inviscid. Again, Bernoulli and Conservation of momentum give different answers...
Sorry about the sign problem, that's just careless of me. So apart from that, conservation of momentum doesn't give the right answer because it can't account for the area change? Does that mean that if there is an inviscid flow, it's just safer to use Bernoulli?
As before, my question is that...
So I've found several instances in which Bernoulli and Conservation of momentum (in Reynolds transport theorem form) give different answers for the study of an inviscid fluid.
Let's consider a simple situation as described in my diagram attached.
Basically a tap/faucet is releasing fluid, which...
Wow, this is non-trivial. I would never have thought to make this connection. This is very cool :-)
Well I have a weird problem with this :-/ I agree with what you said about the every-day examples but if the RH of the surroundings is less than 100% and that causes evaporation from things...
So I just finished reading up a few sources to make sure I have everything. I have 2 remaining questions that I can't seem to answer on my own. It would be great if I could get some clarification on those points.
1. Let's say we have a bowl of water at 20C...in most problems we consider the...
Yeah, that was what was confusing me...since the temperature of the walls in any room we inhabit is less than 100C, according to my initial thoughts, there should be condensation on every wall, which there isn't.
But I'm shocked at how much I lack a fundamental understanding about what's going...