Matrices Quick Tip for Rotating and Reflecting

Quick tips for remembering the matrices that rotate and reflect in this free math video tutorial by Mario's Math Tutoring. We go through reflecting over the x-axis, y-axis, y=x, Rotation 90, Rotation 180, and Rotation 270.
0:24 Technique for Remembering the Rotation Matrices
0:53 Definition of the Identity Matrix
1:19 Rotation 90 Degrees
1:49 Rotation 180 Degrees
2:12 Rotation 270 Degrees
2:25 Reflection Over x Axis
2:40 Reflection Over y Axis
2:55 Reflection Over Line y=x
3:07 Reflecting (3,1) Over y=x
Related Videos:
Coordinate Rules for Rotating and Reflecting (Not Matrices)
• Rotation & Reflection ...
My Video Playlist of More Matrices Videos
• Matrices Video Series
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[@MariosMathTutoring]

Like this video? If you need more review on multiplying matrices see the examples in the video I did here: kzbin.info/www/bejne/mWKZqaafiLeVgdU

[@romnyeverett7758]

this 4 minute video > a whole month of my additional mathematics class

[@MariosMathTutoring]

Wow! That’s awesome! Glad my video was able to help you!

[@siderminerkgl8193]

He could just simplify all this in 2 mins by presenting any θ with the basic formula. [cosine θ -sine θ] [ sine θ cosine θ]

[@xiangzibee963]

Lmao

[@arishbamemon8929]

@@siderminerkgl8193 It could but not everyone is allowed to use calculators for their classes.

[@siderminerkgl8193]

@@arishbamemon8929 If you know the graph plots and the tables of sine and cosine, you can easily find the values for multiples of π/6 angles.

[@AdulTFansClubMan]

extremely clear concept, you helped me shorten the learning time from 2 hours to a few minutes

[@MariosMathTutoring]

+Chinchi. W that’s great! Thanks for letting me know. Glad my channel helped you.

[@priyambandyopadhyay5254]

Thanks a lot. I was having extreme difficulty in understanding these concept, but this video proved a boon for me. Extremely thankful to you.

[@MariosMathTutoring]

You’re welcome Priyam!

[@dalisabe62]

This is discrete rotation by a right angle. If we wish to achieve continuous rotation by some random angle x, we replace the ones in the rotation matrix with cos(x) and sin(x) associated with the proper sign. Thank you so much for this presentation. It was very informative and stimulant.

[@christianpeterson6183]

thank you for helping. i came back from covid into a test of things i didn’t know how to do. now i fell better for my retest

[@sumyazakir2617]

You're a life saviour. I didn't have problems with maths but remembering the matrices was the problem and now it's all good now. Thanks to you!

[@MariosMathTutoring]

Glad my video helped you Shumya!

[@ronaldrodriguez5144]

Beautiful !! I finally understood this concepts !

[@olliecole7163]

Thank you so much, this is so clear

[@Saad-rm8sd]

And my teacher was like just memorize it.

[@MariosMathTutoring]

Glad my video helped you.

[@heartlock1278]

IKR, my teacher also tells us to just memorize, it will be so much better for understanding it

[@lohanygarcia2761]

Love this video! Very clear and easy to understand!

[@MariosMathTutoring]

Glad you like my rotating with matrixes video Lohany!

[@muhamadhaydar8419]

invaluable explaining

[@MonicaMLBH]

Excellent video! Thank you!

[@MariosMathTutoring]

You’re welcome!

[@disasterstruck]

i have a further maths exam in an hour you have just saved my life

[@Vinit_Ambat]

Superb explanation!

[@muhamednajeebk613]

Very simple explanation...thank you very much...

[@mohanadmohamed6460]

Easy to understand Thx, You help me alot.

[@MariosMathTutoring]

+Nodyz HFC your welcome. Glad my video helped you.

[@ashishkumar-bt8he]

Thanks sir for such an easy concept

[@estrillar.5379]

thank you so much! i'm self studying algebra 2 over the summer and this helped a lot

[@MariosMathTutoring]

Estrilla, check out my Algebra 2 video course for sale here: mariosmathtutoring.teachable.com/p/algebra-2-video-course

[@myb278]

Thank you so much this is the content i love, simple and easy to remember

[@Dcoy-hq6fz]

DIOOOOO

[@Ash-bf3qx]

Thank you!!! You've earnt yourself a new subscriber :)

[@haroonrasheed1144]

You make it very easy to understand and saves a lot of my time.

[@MariosMathTutoring]

Great! Glad my video and channel are saving you time and helping you! -Mario

[@lulukevin2013]

thanks for your helping sir..

[@joandy2749]

Thanks a lot... I finally understand that.

[@MariosMathTutoring]

+jo andy great! Glad my video helped you.

[@heartlock1278]

SUBSCRIBED and put a THUMB UP for your fantastic explanations! I can finally understand the matrices without memorizing the formulas and living in fear of forgetting it. TYVM!

[@MariosMathTutoring]

Your welcome! And welcome to the channel!

[@sadianoreen5439]

Superb excellent method

[@Cynxbr]

Absolute Legend

[@torb69]

Thanks , I appreciate your hard work.

[@MariosMathTutoring]

Your welcome! Glad my video helped you!

[@mk0925dolcemusica]

Thank you for your wonderful explanations!!! I am learning matrices by my self because I will be taking PreCalc next year, your videos help me:) Thank you so much!

[@MariosMathTutoring]

You’re welcome! Glad my videos are helping you. Check out my matrices playlist for an organized set of videos on matrices.

[@BluDrop5]

Thank you! This was very helpful!

[@MariosMathTutoring]

You’re welcome! Glad my matrices Video helped you!

[@hyojeongjang3414]

Thank you so much for this! I was trying to memorize this so I could teach my daughter and this really helped😆 thank you again!

[@MariosMathTutoring]

You’re welcome Hyojeong!

[@eduardorivera508]

Amazing! It took my professor two lectures to explain this and I didnt understand it until now. It's awesome how clear that was! Thank you! Will you be doing any college level math videos? Multi variable Calc? Diff. equations?

[@MariosMathTutoring]

I’m glad my video helped you! Not sure yet what other videos I’ll be producing in the future but glad these ones have been helpful!

[@justjacqueline2004]

Succinct to the point,how refreshing.

[@MariosMathTutoring]

Glad you liked the video!

[@mindovermath2042]

I found you through the suggested videos. Your videos are vey informative! I just made a KZbin Channel due to your inspiration. Keep up the Videos! Just Subbed!

[@nurulsolehah6801]

Thank you so much. This might just save me my Maths grades.

[@MariosMathTutoring]

You’re welcome!

[@davidj.cranman3770]

Very helpful and well explained!

[@MariosMathTutoring]

Glad my video helped you!

[@ImranKhan-kz9qo]

great video really helpful. I have a question, when you rotate 90 degrees why do u go anti clockwise and not in clockwise direction?

[@snehalchow5311]

You're unbelievably awesome, You have saved my life!

[@MariosMathTutoring]

I’m glad my video helped you Snehal!

[@yaweli2968]

I wanted to like your video multiple times but realized it wasn’t rotationally possible.Thanks.

[@barnabasmuluboka2543]

Thank you, very much.

[@MariosMathTutoring]

You are welcome!

[@hamzazia6763]

EXCELLENT VIDEO SIR!! ALWAYS HAD A PROBLEM WITH THIS CONCEPT BUT NOW UNDERSTOOD IT VERY WELL....THANK YOU AND KEEP MAKING SUCH GOOD VIDEOS!!!!!!!!!

[@MariosMathTutoring]

Glad you liked my video Hamza!

[@albertibekwe2147]

Thanks this was needed

[@MariosMathTutoring]

Your welcome. Glad my video helped you.

[@tuckfield656]

Beautifully done

[@MariosMathTutoring]

+Henry T thanks

[@someonefromnomansland]

I LOVE YOU THANK THANK YOU SO SO SOOOOO MUCH [cries NO more in Spain (the s is silent)]

[@ismaeltapia7238]

Wow easy to understand

[@MariosMathTutoring]

Glad my video made this concept easier for you Ismael!

[@nirdeshlamsal7108]

thank you sir... i was struggling for a month to get this now i got it

[@MariosMathTutoring]

Awesome! Glad my video helped you Nirdesh!

[@nurulsolehah6801]

Right? Thankfully, I found this video in time.

[@MariosMathTutoring]

Glad my video helped you Nurul!

[@shehrozbabar7411]

thank you so much!!

[@MariosMathTutoring]

Your welcome!

[@quietworld6870]

Very clear concept thanks

[@MariosMathTutoring]

You’re welcome Nurul!

[@Amy-tw3zh]

Genius explanation !

[@MariosMathTutoring]

+Amanda O glad my video helped you!

[@dylan-kt7kd]

i dont understand why school teachers teach so blunt, no proof or intuition for anything making math way harder than it should be. That being said im grateful that channels like this exist

[@shayan144p]

I came here because my matrix was extremely off due to the fact that I wrote one point wrong and I legitimately thought I was going dumb lol I watched the video and corrected the mistake, thanks for helping me out Mario!

[@sarahelmubayed390]

very helpful, Thank you

[@MariosMathTutoring]

Your welcome... glad my video helped you...

[@meicai2948]

thankyou!! very useful

[@MariosMathTutoring]

You’re welcome!

[@ElementalDj]

Thanks Mario, very helpful.

[@MariosMathTutoring]

Your welcome! Glad my video was able to help you!

[@alfiemarshall9224]

great video mario

[@MariosMathTutoring]

Glad you liked the video Alfie!

[@farisnauthoo1170]

Thank you very much you made understand this

[@MariosMathTutoring]

Glad my video helped you Faris!

[@farisnauthoo1170]

So by the way do you do solutions for o level

[@relaxdream3282]

I have a question if am given a matrix and ask to find the value rotating through 90 ° can i multiply by the value given above to have the answer?

[@thegamingtaco6283]

I have a question, is there a particular matrix that will allow you to reflect a vector across this plane (x+y+z=1)

[@dage1996]

Very nicely explained.

[@MariosMathTutoring]

+Hamza Khalid Thanks!

[@sjard97]

My new math guru.

[@MariosMathTutoring]

+Samantha Jardeleza glad you like my channel!

[@camilojarac]

Great explanation! Thank you so much :)

[@MariosMathTutoring]

You’re welcome Camilo!

[@DRCSUDHAGAR]

very easy method. Subscribed and i shared with my students.

[@MariosMathTutoring]

Great! Welcome to the channel. Glad you liked the video!

[@amanbineet731]

Exellent explation

[@MariosMathTutoring]

Glad you liked my rotation with matrixes video Aman!

[@colorfulcodes]

Interesting.

[@IbiDon]

sooo helpful

[@MariosMathTutoring]

Glad my video helped you!

[@DeepakKumar-dh2eb]

wah sir ji

[@vponnejork5831]

jesus you are the best.

[@erik9817]

Hm, if I program this into a game, I should be able to rotate things?

[@vitrovogan9635]

Thank you

[@MariosMathTutoring]

You’re welcome Vivek!

[@abdullahfaisal8353]

Thx man!

[@MariosMathTutoring]

You’re welcome Abdullah!

[@VishalSingh-mq6vh]

Awesome

[@MariosMathTutoring]

Glad you liked the video Vishal!

[@kawingwong798]

Thank you sir!!!! I finally understand what is going on after watching a bunch of youtube channels...

[@MariosMathTutoring]

Glad my video helped you Ka Wing!

[@chitsfitss]

Thankyou sir :)

[@MariosMathTutoring]

+Abigal Scott your welcome

[@cikguhassan]

does it has to be only anticlockwise rotation ?

[@MariosMathTutoring]

No...either direction it will work...

[@muhammadarhamnaeem180]

awesome

[@MariosMathTutoring]

Glad you liked the video Arham!

[@VeritasEtAequitas]

But how do you know these without memorizing each of them separately? Is there a way to look at a 2x2 transformation matrix and determine what it does without plotting points? I see for the rx, refelction across x the y values invert, and the "1" in the identity matrix has inverted value. Good. Same for the ry. Beyond that, I see no rhyme or reason, nor does my text explain it, nor does Khan Academy in the section I'm following along with there.

[@mranishkjohn]

Great video which ends in 4 minutes.

[@MariosMathTutoring]

Thanks! Glad you liked the video.

[@vibhutg1919]

i didnt understand the matrix over the y axis can someone explain it

[@superkillergaming2419]

Sir you look like my favourite 🌟

[@tariqullah7012]

thank you Sir a lot,, May ALLAH bless u

[@MariosMathTutoring]

Your welcome Tariq! Glad my video was able to help you!

[@dghffvb]

Lovely..

[@MariosMathTutoring]

+prakash shanker glad you liked the video

[@ritesha8050]

Thanks, the rotation is anticlockwise? If it's clockwise, we have to do the same thing but for 90° clockwise

[@ritesha8050]

I subbed

[@MariosMathTutoring]

Yes you got it! Welcome to the Channel!

[@kamrulhasan6004]

Sir i have a question If A=[1 2 2 1] And f(x)=1-x/1+x then what is the value of f(A)=

[@mr.es1857]

Thanks again for all of your work, in this entry I would like to ask for your help I have a doubt that is making me struggle and I have look at a few books but some of them don't mention this and in the best case they just give a few details and I need bit more. I'm looking for matrix logarithm of rotations and if you could guide me in this giving me any advice, any paper I would be very thankful. The books that have helped me the most for this are: "Modern Robotics from Kevin Lynch" and "A Mathematical Introduction to Robotic Manipulation from Richard M. Murray " Thanks in advance c:

[@MariosMathTutoring]

Wish I could help you but what you are describing is beyond what I know...

[@mr.es1857]

@@MariosMathTutoring maybe you can see it as the inverse of the the exponential coordinate representation of a rotation matrix , knowing that if you apply the matrix logarithm to the exp coordinate of a rotation matrix you get back the rotation matrix .

[@Bingerz11]

Thanks this helped a lot. Jacsin sixth form england

[@MariosMathTutoring]

Your welcome! Glad my video helped you!

[@mdalisaifulapek427]

Thanks

[@MariosMathTutoring]

Your welcome!

[@mdalisaifulapek427]

+Mario's Math Tutoring 😊😊😊

[@samud7041]

💕💕💕

[@ms12earth]

Thanks sir, but where are u from

[@MariosMathTutoring]

U.S.A.

[@ms12earth]

Sir I have a KZbin channel too so can u help me increase subscribers in my channel named MS12 Earth. It would be a great help. My Channel is not good as yours, thanks

[@donegal79]

Good video.....but no substitute for listening in class the first time Seriously, if you didn't get it when explained in regular class then coming over her to watch this and exclaiming OMG, now I understand" is a bit pathetic really. In any case, well done sir, well explained,,,,its good for your career that there are people who just don't take enough of an advantage in their own class time.

[@yassir-5605]

JT you can't always follow classes Sometimes students are too noisy for you to make it out Or the teacher's awful

[@saladbee]

Nina swali determinant is supposed to negative

[@Kurosaka]

noice

[@MariosMathTutoring]

Glad you liked the video!

[@Kurosaka]

@@MariosMathTutoring your welcome

[@affanahmed9441]

cheetah laga

[@alias_peanut]

cut off 😑😑3:10

[@waz1136]

Thank you so much! This video was very helpful.

[@MariosMathTutoring]

Your welcome! Glad my video was able to help you!

[@owenlee3144]

Mario's Math Tutoring *you're welcome*