Idea behind inverting a 2x2 matrix | Matrices | Precalculus | Khan Academy
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What the inverse of a matrix is. Examples of inverting a 2x2 matrix.
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can we pls stop for a moment and realize tht this video was actually filmed 12 years ago!!!
ur kidding man omg,since back then he was always posting these awesome vids to help ppl AND FREE!! thank you so much for that sal
I just saw the video and it's now 2024, that's 16 years! I can only imagine who's going to see it next!
I had a linear algebra course when I started studying 7 years ago and I used these videos.
Now 7 years later I have a computer graphics course that uses matrices and here I am back at this video to refresh, and it's still as solid as I remember
You have truly helped millions of people I hope you understand that!
Outstanding
91.7% on my matrix exam , the rest of the points went to carelessly leaving out neg signs on 2 problems. Thank you :D
Kaylah Miranda congratulation
+Kushal Gaddam xD
Congrats. I know I’m a little late haha
that is effectively 100% bravo! that's how I'm taking it.
Not all heroes wear capes, thanks!!
What if he *is* wearing a cape and we just can't tell ....?
Its because the capes get sucked into the engines... geez, didn't you see the movie?
this is literally voodoo,
literally just writing down the formula makes no sense how the
c and b get inverse signed and why diagonal multiplication is a thing
NeostormXLMAX “my power can disturb your mind, Superman !” “Shut up! Matrix.”
khan= the only reason I am passing
"Khan Noonien Singh is the most dangerous adversary the Enterprise ever faced. He is brilliant, ruthless, and he will not hesitate to kill every single one of you."
- Spock, 2259 (Star Trek Into Darkness)
Thank you, thank you, thank you, thank you!
Before this I watched a 15 minute long video on finding the adjoint of a 2x2 matrix, there was a bunch of unnecessary steps, and at the end I still didn't understand it. I was pissed, my time was wasted, I felt dumb, and it's not even that hard. What the hell did they put me through? You explained it in one sentence that made perfect sense. Now I can find the inverse of 3x3matrices, I watch your other videos, I know if infinite sums converge or diverge. I don't bother with any other videos. You rock!
-15+8 =7 (it's an 8, not a 9)
did u mean -7?
OMG I suddenly realize the time!.12years ago？！I was in the kindergarten😂
陈小艺: 我也是
Impossible
TRYHARD RACCOON 嘻嘻
As a freshman CS student who has never been taught matrices in school I really appreciate these videos...
I love khanacademy so much!!!! I don't know what I would do without you guys so I donated :)
12 years later and the black and green theme still gives me nostalgia
having a math test tomorrow and i am refreshing my memory.god bless you,you are a hero
I learned this over 3 years ago from a Greek Professor at Bath University and it was so hard to follow. His English wasn't great and he blazed through it. I had to write so damn fast my paper caught fire ;) I used this video to refresh my memory and it was much easier to follow. Who needs £9000 a year tuition fees when TH-cam is free and you can pause the video? University is highly over-rated with respect to quality of teaching.
you are a godsend angel! grtz from holland!
I like how you say solving a 3x3 "is even more fun". Positivity is a much better tool than the tendency to use words like complicated or difficult. :)
I was absent for a week during my Alg2 class and had to cram for a test coming up, I found all of your videos on Matrices really useful and I actually learned how to do my work I was absent fairly easy.
+1 Sub!
Wow, that was simple. It was a little bit confusing, but I caught up much more quickly here than I would have in my classroom with my COLLEGE professor. Thanks for putting this video up.
Practice, Practice, Practice!
God Loved us so much that He sent us Sal. What a gift to teach this man has, great is his reward in heaven. Sal should be named teacher of the millinium, God bless you Sal and God bless you cousin, I believe who you were teaching initially... :)
OMG THANK YOU SO EFFIN MUCH, I HAVE EXAMS TOMMOROW AND MY TEACHER SUCKS AND YOU JUST MADE THIS SO SO SO SO SO SO SO SO MUCH SIMPLER
Great explanations! It's very nice to have a source to go to for a refresher as apposed to flipping though complicated definitions in textbooks!
"but this is good exercise for multiple parts of the brain"
that line might change my life...i just realized my problem...i had always been the math genius when i was young so i became over confident....i used to find maths so easy that i never had to even try to understand something...as maths became complicated i found it becoming harder..this is because i usually did not try to spend time on a question if i dont understand it because i wasnt used to it...I DID NOT EXERCISE MY BRAIN!!
I understood 100 times better this lesson in english than my - 6 hours in a week - lesson in french (and I don't really speak english ). Amazing.
This vid helped me 100%. I understand inverse matrices after a 14 minute video. sweet!
My Professor made it seem much more complicated than it actually was. I was having so much trouble figuring this out--searching my textbook and my notes--until I saw your video. Your explanations were so easy to follow, and it helped me realize just how simple finding the inverse is.
Thank you very much!! Now I'll have no problem on my upcoming exam. :)
thanky you, something that's confused me for years is now crystal clear. wish you were my algebra II teacher, i would've learned something
I passed my first math course with you guys, I'm going to pass again by watching you again. Def donating soon
Thanks, Khan. You are the best teacher I've ever had.
I spent all the night trying to understand the Gauss-Jordan method, but this seems to be more straightforward. Thanks a lot, this has been very helpful!
this is seriously awesome. I really wish I could just get a degree from Khan Academy than UCF. way easier to learn the same stuff here than the way they teach there
thanks man
ur explanation is better than the ones taught at school!
thank you for these matrix videos they are like having my math teacher at home without his moving to fast and being a creepy tall italian old dude.
No joke... You are the only lecturer that I pay attention to. I dont even go to my math lecture anymore. And I'm in a top 5 engineering school. You rock my face off. Its that extreme, I had to go oldschool.
THANK YOU!!! FINALLY EXPLAINED BY A HUMAN BEING!!! IT FINALLY MAKES SENSE!!! :)
I like this. I got a bit confused with the book after a while. The book plus your videos is illuminating.
:D Youre much better at teaching than my professor. Thanks!
Oh my lord. And I just realized.... unlike my professors, I can pause you awesome instruction when I need to text! Ok, you are officially my hero.
i have a exam today , and that was really really helpful
thanx , wish me luck
You are the best teacher alive.
if i had a dollar for every pixel on this video... id have 1 dollar
@@elyria9788 that's.. not how it works..
@@elyria9788 lost me there at the end
Sick how you made such a complex topic so simple. Big thanks!
I didn't know he used MSPaint to do this...this guy is AMAZING! I love his teaching...he makes everything so clear that someone could learn this entire subject just from his videos. Great job man! :D
My man, on behalf of all the IB students in Iceland, I would like to thank you personally.
thx for helping me it will help me understand algebra 2 much better
you are god teacher that every student wanted explains concepts and than sums
Your videos are so helpful. Thank you so much!
Thanks mate for the 2x2 matrix inverse Help!!! I got my final for tomorrow bet this will help me abit!!
Two big differences I noticed with these videos as compared to class. 1. I actually learn through these videos and can go at the pace I need to. 2. I can drink as much beer as I want when I'm doing math.
Hey guy, I am 44, and now I finally understood clearly ... Great video.
Understand, not understood.
Thank you Khan, you're the best, keep helping people me.
Thank you Khan, I'm so grateful! U saved my life since I was in high school. Today u saved my life again for my next test! I own you man
this is great i don't wanna go to lectures any more :) you are awesome
We've had the privilege of listening to God speak about math.
this video was ridiculously simple
not only r u an amazing virtual teacher but you just made sense of my double further maths class today
Thank you =
learned more from this video than a month in my math class.
khan, you are doing awesome job man. I am fan. Keep doing the great job.
I found this interesting! It was more fun than the logarithmic equations I do,I give you that.
thanks for making a brain boggling concept more clear….great job!!
Thanks . Because of this video my matrix concept is good and i can solve any type of matrix question
I remember 2008.... i wore glasses back then because i thought my eyes were fucked, but legit best tutorials ever i learn so much from khan cheers guys keep it up
You mean Minaminoto, i.e Pie face, yea he does say stuff like Inverse matrix, radians and all that, he is really funny.
Anyway, this is fantastic. I am revisiting matrices for my exam next month and this is really helping out. I remember proving how the determinant was ad-bc the most horrible part with 2 pages of algebra or something. But anyway, I will check out the rest of the videos.
Great explanation and video. Thanks a lot.
Useful for further maths CIE 9231 as well! I recommend Khan Academy!
thx for the vids man, im learning this concept for mathematics C next year
dude u r totaly good at this & thanks for the video
OMG that was very hard!!!
Thank You so Much
Thank you very much for this video! It was a good basic video regarding the identity matrix and the inverse of a matrix!
very nice to be able to come back and revise these things with good, clear, concise explanation. thanks Sal!
All your math videos are great. You make math look simple and easy. Thanks for posting these videos.
This was really good, it was a refreshing way to revise (or get re-educated in my case), thanks a lot.
By the way, what program do you use, it looks fun to work on?
In this case |B| does not mean absolute value of B, it just means determinant of B. It just happens to use the same symbol. So |B| can be positive or negative.
this guy is the best.for real
No, you may want to rethink this a bit. You're correct that -4*2 = -8.
However, when substituting (bc) with -8 in the determinant formula, ad - bc, and (ab) as -15, the result is:
(-15) - (-8) = -15+8 = -7
The error was misinterpreted determinant formula, ad - ac, as ad + bc.
I hope this explains much.
Sal, you're a legend! Thank you.
Thank you, sir. Very helpful, straight forward refresher.
Thanks so much you covered exactly what I didn't understand in my Alg 2.
this guy is AWESOME!
Nice video, the only part i didn't follow to well was multiplying matrices (only just watched your other video) but in the end i times the matricies the other way around and got
(15-8)(1/7) (-12+12)(1/7)
(10-10)(1/7) (-8+15)(1/7)
or 1 0
0 1
:D
However you could have chosen a similar example for your first video.... but in a way I think if you did i wouldn't have remembered as much... like 1/ad-bc d,-b,-c,a
You guys are doing amazing job all around
@capitandelfuego no the transpose is the rows and columns switched.
So if A = |a b|
|c d|
The transpose of A would equal
|a c|
|b d|
grateful ♥♥thax a lot ..khan academy
Thank you so so much!! Helped me a lot!!
Linear Algebra midterm tomorrow. Haven't paid attention in two weeks. Sal i really need your help lol
Thank you so much. You are doing such a noble act. May Allah be pleased with you
13:38 your happy because you didn't make a simple mistake and wouldent have to film it again
haha! so fuuny... even the brilliant got confused after solving tons of math questions lolss... now i don't blame maself for getting small errors in ma tests lolss
I enjoy learning from you.
EPIC but u should make a video for cramming for SAT's
It's really easy now!
Well, this is a first year course, so it's assumed that you can learn it with fair ease.
dude... i love you so much right now. So very much.
I wish this video had an updated version with better resolution.
Im glad you used green colors, reminds me of Matrix
i have an exam in this today... i think after watching this i might actually pass :P
Thank you so much
Very informative and clearly explained.
thanks you very much, I appreciate the help. My TA isn't the best.
Gr8 stuff... yet again.
from uk
this saved me
i would like to emphasize "saved" but alas, i cannot express it through mere characters
TY it helps a lot!
i find this fun actually. its so odd that its actually fun. takes away from normal math patterns
Love your videos Sal! Thank you!
Thank you now it makes sense
thnx really helped a lot