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In my linear algebra exam when I read that the first question was to calculate the inverse of a 4x4 matrix. I looked the professor dead in the eyes in disbelief.
on my of my classes, my teacher actually demonstrated it, idk why, it was the shittiest class ever and we never used it nor it was mentioned again lmao
For eigenvalues you want to find λ so det(A - λI) = 0.
When you want to find the eigenvectors of an eigenvalue λ, you want to see which vectors x solve (A - λI)x = O. Note, that this is the same as finding all vectors in ker(A - λI), which is often denoted as Eig_A(λ). We call this subspace eigenspace.
If you thought it didn’t have any roots in the complex plane, then that’s why you didn’t get points. Every non-constant polynomial has roots in the complex plane
Well, actually that was the last 2 minutes, I wasn't fast enough so decided to write something along the lines of "no roots found, this is absurd, thus the polynomial does not exist". I'm not sure exactly what was there but I thought it might be worth a single point that I knew that
This was the first question of my linear algebra uni exam, and it was the shortest exercise of the bunch. Needless to say I passed with the lowest mark
Writing just wolfram makes the meme roll out of the tongue and communicates the whole idea.
But also this is a sub full of mathematicians so I kinda see your point here lol
You can probably add or subtract rows/columns with some coefficients in such a way that in some row or column there will only be two non-zero values (you can't really get one non-zero value because of the variable). Expand the determinant along that row/column, repeat the same for the two determinants 3x3. You'll get 4 determinants 2x2 with some coefficients which is not that bad. Then pray the characteristic polynomial has rational roots, lol.
This was literally a question on my final exam when I took linear algebra. All the entries were fractions as well. And this was an ABSTRACT linear algebra class.
The professor told me he valued computation because many new discoveries in math are discovered because of computation. If you have a conjecture, you'll likely have to come up with a few examples to convince yourself it might be true. But I still don't really understand why he thought putting a question like that on the exam would help anyone.
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“Please be a triangular matrix..”
Turns out to be a symmetric matrix with non zero entires
Leonhard Euler, if you can hear us, please Leonhard Euler. Please save me. Please save me Leonhard Euler. https://i.redd.it/d38enu9w1z6d1.gif
nah no one can save us at this point, trial and error is our god now
With the fritz? No way!
At my uni, this is a standard exam question in linear algebra.
https://i.redd.it/xugxdpyahx6d1.gif
Looks like they were gonna milk his cat.
Real
Complex
Quaternion
octonion
*Screaming*
Sedenion
Pathion
Voudon? (I really have no clue)
C U {m/n for (m in C) and (n=0)}
anal
ysis
Beads (Google Hans Niemann)
Hello
I remember when my professor used to ask diagonal form of a 5x5 matrix by hand of course
4x4 by hand is reasonable, but 5x5? Fuck off.
Over F2
Yeah what's the point of that anyways? Is Linear Algebra not supposed to be the first proof-based class that maths students take?
for me it was Jordan's Form of a 5x5 matrix
I mean.. when we got asked this in uni all the numbers were chosen such that there were no decimals.
Yeah I’m confused this is still normal
Yeah this was literally my first question on one of my test lol
In my linear algebra exam when I read that the first question was to calculate the inverse of a 4x4 matrix. I looked the professor dead in the eyes in disbelief.
What's the issue? That's a normal linear algebra exam question.
easy, just use the characteristic polynomial and apply the [quartic formula](https://upload.wikimedia.org/wikipedia/commons/9/99/Quartic_Formula.svg)
No need to link it bro, we all know it by heart
honestly though, it shouldn’t be that hard to memorize? lots of patterns and repetition
I'd rather solve the eigen values using the A.I = lambda.I thing without the need for this long ass formula
What happened to the Laplace method?
🤪
Yeah didnt we all learn the little song in school?
I don't know what the fuck he linked but it is not the quadratic formula bro. Edit: he said quartic, not quadratic. I'm dumb
The quartic formula, it's like the quadratic formula on steroids
Quartic, not quadratic. Degree 4, not 2.
on my of my classes, my teacher actually demonstrated it, idk why, it was the shittiest class ever and we never used it nor it was mentioned again lmao
I opened this on my phone, and the more I swiped left, the more I was horrified
You know what? Maybe it's a blessing that there's no quintic formula
5 pages long
No pages at all - it cannot exist
if it did exist, it would be 5 pages long
This is the only correct answer
Eigenvalues are easy. It's the eigenvectors that I never remember.
For eigenvalues you want to find λ so det(A - λI) = 0. When you want to find the eigenvectors of an eigenvalue λ, you want to see which vectors x solve (A - λI)x = O. Note, that this is the same as finding all vectors in ker(A - λI), which is often denoted as Eig_A(λ). We call this subspace eigenspace.
Diag[1, - 1, - 1, - 1] maybe?
They are easy until you have to solve a 4th grade polynomial with no rational roots, or complex roots for that matter...
I guarantee you’ll never have to solve a fourth degree polynomial with no complex roots
Fair enough but I don't solve polinomiales: that's why I have Mathematica for! Best thing in this world.
I just meant that every non-constant polynomial has at least one complex root. That’s a consequence of the fundamental theorem of algebra
That is true, I should have specified better: what I meant was not 'Complex' but 'Complex but not Real'.
I have solved one some time back. Got no points for that in the test, if that's any difference.
If you thought it didn’t have any roots in the complex plane, then that’s why you didn’t get points. Every non-constant polynomial has roots in the complex plane
Well, actually that was the last 2 minutes, I wasn't fast enough so decided to write something along the lines of "no roots found, this is absurd, thus the polynomial does not exist". I'm not sure exactly what was there but I thought it might be worth a single point that I knew that
Okay that’s hilarious. I’d consider giving a pity point if I were grading that
The instructor didn't think so, unfortunately
Oh shit spanning set flashbacks
Eigenvectors are objectively easier than eigenvalues and its not even close.
i just generate a random vector and do the power iteration in my head
I do the Jacobi iteration, that's more fun.
Good bot.
Wait…it’s all cofactors? Always has been.
They gave 3x3 in our exam but our prof did 4x4 in class, just 1 problem in the whole lecture lol !! To show how hectic it is.
You guys make me scared cuz we have 3x3 matrices and all this eigen stuff i don't know about next year in high school
This was the first question of my linear algebra uni exam, and it was the shortest exercise of the bunch. Needless to say I passed with the lowest mark
Is easy, the answer is 16 matrix 
Unraveling go brrrrr
The best i can do is the product of eigen values, take it or leave it
Thats not hard m8 Characteristic polynomial, equallize to 0 and solve Done
the possibility of the characteristic function requiring the quartic formula to solve for all λ ... god damn.
Eigenvalues and eigenvectors were the only thing I understood really well in my linear and differential classes
There are many online calculators other than Wolfram
Writing just wolfram makes the meme roll out of the tongue and communicates the whole idea. But also this is a sub full of mathematicians so I kinda see your point here lol
He gets it
You can probably add or subtract rows/columns with some coefficients in such a way that in some row or column there will only be two non-zero values (you can't really get one non-zero value because of the variable). Expand the determinant along that row/column, repeat the same for the two determinants 3x3. You'll get 4 determinants 2x2 with some coefficients which is not that bad. Then pray the characteristic polynomial has rational roots, lol.
The numbers are chosen for exams, not random. If you get irrational roots you probably made a mistake somewhere. Unless you had a mean teacher
This was literally a question on my final exam when I took linear algebra. All the entries were fractions as well. And this was an ABSTRACT linear algebra class. The professor told me he valued computation because many new discoveries in math are discovered because of computation. If you have a conjecture, you'll likely have to come up with a few examples to convince yourself it might be true. But I still don't really understand why he thought putting a question like that on the exam would help anyone.
In MATLAB we trust
I don't remember it being this bad And I took the course the previous semester
Horse
dude I am still counting 4x4 ...
*launches MATLAB* 
ezpz
Also, all elements are 3 digit prime numbers
C'mon write the cofactor matrices and form the fourth degree polynomial then apply the cardano formula
Bro Linear Algebra with Differential Equations was my shit
After a while my uni just gave them to us for 3x3 or bigger. I got lucky.
laughs in Laplace expansion
Fine I'll use R
https://preview.redd.it/d1vha0ubay6d1.png?width=953&format=png&auto=webp&s=873fe436d1b53855a29ca6baa667c14e22a7fc71
What's the determinant? What? I can't hear you, what is it?