I got it. Many thanks @leslietownes :) I also saw the link shared by @PM2Ring: it says the same thing that you were saying earlier: sequence of rationals converging to any real number.
from 1-18 minutes , the professor is discussing Gaussian elimination and suddenly around at 25 minutes he is trying to obtain the same results through matrix multiplications . Why ?
the vibe of row reduction using elementary matrices is definitely one that is only acquired with experience. i found it helpful to use a computer algebra system where you can rapidly input matrices and see what the products work out to. nothing more fun than stacking up a product of three or four elementary operations on the basis of your mental view of how you'd row reduce, hitting the matrix with it, and seeing it work.
@TedShifrin Yeah , I did talk this with you before starting the series. You said that your lecture series is more proof oriented , but then I get the advantage of asking doubt from the instructor who taught it. how cool is that ? Also , i find strang lectures to be a bit fast paced for me...
Hello! Does the condition $\varphi(s):L_{\nu,q}(R^+)\to\mathbb{C}$, where $\nu,q\in\mathbb{R}$ and $q\ge2$ suffice, to ensure that the Inverse Mellin-Transform of $\varphi$ exists?
Right. I remember. I personally think my lectures are clearer than Strang's, although I admire him deeply. My lectures may be fast, too. I'll look up the numbers for this topic.
Try Lectures 33, 34 here. Go back to 30-32 if you want.
I do not remember exactly, it was 10 years ago in my bachelors when i read the topic. But I remember that the solution of those equations lead to eigen values and vectors...
Hi I have a question about solvability of a problem. Given a triangles angles x, y and the side c shared by both angles and knowing that sin(y)*a^2 = sin(x)*b^2 where a and b are the sides opposite to y and b respectively can we solve for all angles? imgur.com/a/Yd87ahD image of the situation. It comes from a part of a real life physics problem I'm trying to solve and I think in theory it should be solvable based on physical intuition, but I can't seem to find a solution.
so you only are interested in finding the last angle? is this triangle just in the plane? if so, you might just need that the angles in a triangle sum to 180 degrees
if so, i think you can conclude from law of sines that $a^3=b^3$ which would make $x=y$ and the triangle isosceles. then i you may be able to get that there is a whole family of "solution triangles" with the family given by the height of the triangle with $c$ fixed
To give context, C is a point of light and A and B measure the intensity, and we know those readings and the distance between the sensors and I'm looking for the angle X at which the light source is tilted
from law of sines, $\frac{\sin(x)}{b}=\frac{\sin(y)}{a}$ and your formula (solving for $\sin(x)$) gives $\frac{a^2}{b^2}\sin(y)=\sin(x)$. Subbing into law of sines, we get $\frac{a^2\sin(y)}{b^3}=\frac{\sin(y)}{a}$ and doing some algebra, we get $\frac{a^3}{b^3}=1$.
i may have made a mistake, in which case im very sorry! but thats what it seems to give
if this is correct (check me please!) then we get $a=b$ and the triangle is isosceles and the height seems to be able to be anything
from the hyperphysics link, you have "E" readings at points $A$ and $B$ on a line from a light source at point $C$ and the goal is to find the angle line $AB$ makes with line $CD$ where $D$ is the midpoint of $A$ and $B$? Is this correct? And the value of $I$ from the light source is known?
Yes the statement of the problem is correct, and no the I from the light source is unknown.
But if you think about having three sensors on a flat table and you move a lightbulb above them, the readings should give you enough information about the bulbs azimuth and altitude angles or is my intuition wrong?
We don't need the distance from the bulb to the table
So only two out of three coordinates in the spherical system
