Detexify

Draw a symbol and get the corresponding code in latex,

http://detexify.kirelabs.org/classify.html

There exists a unique polynomial of degree $n$ passing through $(n+1)$ points in a plane.

So, if one we have a one-point say $(a,b)$ then clearly $f(x)=b$ is the (unique) polynomial of degree $0=1-1$ through the point. Now, we all know, $\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$ is the unique polynomial (put $y=f(x))$ of degree 1.

Hence we sort of asking the general question and fortunately, the answer is yes, which one proves using the Vandermonde matrix and of course Lagrange Interpolation formula actually gives the polynomial.

Here is the solution,

Reference:
https://math.stackexchange.com/questions/837902/prove-there-exists-a-unique-n-th-degree-polynomial-that-passes-through-n1-p


Inverse of a Vandermonde Matrix : ​https://proofwiki.org/wiki/Inverse_of_Vandermonde_Matrix 

Alguns Provas

https://www.dropbox.com/s/hgk6soslss5gvhz/P2-T5.pdf?dl=0

Gabarito Mat 137 e 140

https://www.dropbox.com/s/xci591aw40b7pgo/gabarito_exame_final_mat137.pdf?dl=0

https://www.dropbox.com/s/sfis345m7h9lojz/prova_gabarito%20%282%29.pdf?dl=0

https://mega.nz/#!dUNDQIKD!HVQwXJgNv2EwwIPypCu0A6s_v0NdFPlX8-wfAfpi_1Y

Plot a graph in $\LaTeX$

Here is the code that you might like to use to plot a graph in $\LaTeX$

$\begin{figure}[h!]

     \centering

     \begin{tikzpicture}[scale=0.70]

     \draw[thick, ->] (-12, 0) -- (12, 0);%asse x, la punta puo' essere > 

     o latex ( o altra roba ma..)

     \draw[thick, ->] (0, -12) -- (0, 12);%asse y

     \draw[thick, dotted] (1,-12) -- (1,12);

     \draw[thick, dotted] (2,-12) -- (2, 12.0);

     \draw[thick, dotted] (3,-12) -- (3, 12.0);

     \draw[thick, dotted] (4,-12) -- (4, 12.0);

     \draw[thick, dotted] (5,-12) -- (5, 12.0);

     \draw[thick, dotted] (6,-12) -- (6, 12.0);

     \draw[thick, dotted] (7,-12) -- (7, 12.0);

     \draw[thick, dotted] (8,-12) -- (8, 12.0);

     \draw[thick, dotted] (9,-12) -- (9, 12.0);

     \draw[thick, dotted] (10,-12) -- (10, 12.0);

     \draw[thick, dotted] (11,-12) -- (11, 12.0);

     \draw[thick, dotted] (-1,-12) -- (-1, 12.0);

     \draw[thick, dotted] (-2,-12) -- (-2 , 12.0);

     \draw[thick, dotted] (-3,-12) -- (-3, 12.0);

     \draw[thick, dotted] (-4,-12) -- (-4, 12.0);

     \draw[thick, dotted] (-5,-12) -- (-5, 12.0);

     \draw[thick, dotted] (-6,-12) -- (-6, 12.0);

     \draw[thick, dotted] (-7,-12) -- (-7, 12.0);

     \draw[thick, dotted] (-8,-12) -- (-8, 12.0);

     \draw[thick, dotted] (-9,-12) -- (-9, 12.0);

     \draw[thick, dotted] (-10,-12) -- ( -10.0,12);

     \draw[thick, dotted] (-11,-12) -- (-11, 12);

     \draw[thick, dotted] (12,1) -- (-12, 1);

     \draw[thick, dotted] (12,-1) -- (-12, -1);

     \draw[thick, dotted] (12,2) -- (-12, 2);

     \draw[thick, dotted] (12,-2) -- (-12, -2);

     \draw[thick, dotted] (12,3) -- (-12, 3);

     \draw[thick, dotted] (12,-3) -- (-12, -3);

     \draw[thick, dotted] (12,4) -- (-12, 4);

     \draw[thick, dotted] (12,-4) -- (-12, -4);

     \draw[thick, dotted] (12,-5) -- (-12, -5);

     \draw[thick, dotted] (12,-6) -- (-12, -6);

     \draw[thick, dotted] (12,-7) -- (-12, -7);

     \draw[thick, dotted] (12,-8) -- (-12, -8);

     \draw[thick, dotted] (12,-9) -- (-12, -9);

     \draw[thick, dotted] (12,-10) -- (-12, -10);

     \draw[thick, dotted] (12,-11) -- (-12, -11);

      \draw[thick, dotted] (12,5) -- (-12, 5);

     \draw[thick, dotted] (12,6) -- (-12, 6);

     \draw[thick, dotted] (12,7) -- (-12, 7);

     \draw[thick, dotted] (12,8) -- (-12, 8);

     \draw[thick, dotted] (12,9) -- (-12, 9);

     \draw[thick, dotted] (12,10) -- (-12, 10);

     \draw[thick, dotted] (12,11) -- (-12, 11);

     \draw (12,0) node[below]{$x$};

     \draw (0, 0) node[below left]{$0$};

     \draw (0,12) node[left]{$y$};

     \end{tikzpicture}

    \end{figure}$

Gmail - Attach email to email!

Ever dreamt of sending a set of emails to another email as an attachment. In case, you did here is the answer to your dream,

https://www.theverge.com/tldr/2019/12/9/21003638/google-gmail-email-attachement-feature-update 

Useful tips to visit Europe

Here is the blog which I found useful for the subject

https://www.nomadicmatt.com/travel-blogs/cheap-ways-to-travel-across-europe-2/ 

One more thing which might suggest the right option for travel within Europe.

https://www.omio.com/ 

Well, I personally like very much the following site for the bus tour,
https://www.flixbus.pt/?_sp=77e2d29c-1cbd-45cc-8b82-b330f1bb1c52.1576447316263&atb_pdid=479e6a8f-1711-4c02-b77d-a1563465a5ce&wt_eid=2157641830588589778&wt_t=1576447316332


Talking about visiting another country, the internet is something very crucial, and that leads to buying a sim card. Well, there are infinitely many agencies begging you to buy their insanely costly sim. I usually prefer buying one in the country I visit. Here is something you might like to do in case you agree with me and you are touring Europe,

https://www.eurocheapo.com/blog/best-sim-cards-for-your-trip-to-france.html

$AA'$ and $A' A$ have same set of eigenvalues.

Suppose $\lambda$ is an eigenvalue of $AA'$. Hence
$\begin{eqnarray*}
AA' \cdot x &=& \lambda\cdot x\\A'A(A' \cdot x) &=& \lambda A'\cdot x\\
\end{eqnarray*}$
This proves, $\lambda$ is an eigenvalue of $A'A$.

A Different Way to Solve Quadratic Equations

No more buying EUROS while visiting Europe!

Friends,

One need not have to buy euros anymore while visiting Europe. There is a bank called N26. There are some countries where you can open this account (Standard account is for free) and they will deliver the card at your doorstep. In Brazil, the bank does not deliver the card currently but soon will be functioning here, as in the news. Although you recede in Brazil, you can open an account as far as you have some address in Europe. You just have to put residency in Europe while you fill in the open account form.

It is an easy process to open an account. Once you are done with it, just make a transfer using an international transfer service to your account. I myself like, TransferWise, in case you want to get yourself a first free transfer, use the following invitation link,

https://transferwise.com/invite/u/bhavinkumarm


Have a nice flight!

Fly cheap all over the world!

Hey friends!

Yeah, we always search for some way to not spend a lot of money while flying. I fly often and hence had and always will have this question of how to get a bang for the buck! Well, I often (PS. In incognito mode) search flights on some sites (written as per my preference),

1. Google Flights and Hopper (This app is just awesome! They have really good tech support.)

2. https://www.kiwi.com/us/

3. Kayak

Furthermore, there is often a problem packing bags while flying. Here is something that might help you,

Hand luggage: This packing trick taught in the Army could beat airline restrictions | Travel News | Travel | Express.co.uk

4 Easy Ways To Use Google Flights to Find Cheaper Flights And Organize Your Trips,

​https://www.forbes.com/sites/advisor/2019/12/13/4-easy-ways-to-use-google-flights-to-find-cheaper-flights-and-organize-your-trips/


5. Go for https://www.seatguru.com/ for reserving your place. It will give you all the information you will ever need to get the best possible seat. Do check-in as soon as it opens. Have a nice flight :)

6. In case you might like to track your flight, you might like to see the following link

https://thepointsguy.com/guide/how-to-track-airplane/

Linear algebra and Machine learning

Check out an awesome article here,

https://machinelearningmastery.com/examples-of-linear-algebra-in-machine-learning/

Take your machine learning skills to another level

https://mlwhiz.com/blog/2019/12/25/prod/

Linear Algebra in Data Science
https://www.analyticsvidhya.com/blog/2019/07/10-applications-linear-algebra-data-science/

Alguns Gabaritos - Matemática UFV

Podem encontrar alguns Gabaritos no link,

Gabaritos

Score a flight upgrade using two simple words

See the following article.

https://fortune.com/2018/02/22/flight-upgrade-tips/amp/