PreCalculus - Matrices & Matrix Applications (33 of 33) Using Cramer's Rule to Find x=? y=? z=?

[@colortalks5133]

Sir, you are KING! you are the best math instructor on youtube. I've been watching your videos since my freshman year and thanks to you I am graduating soon.

[@cooldown6077]

I finished the playlist today. I bet anything, this is the best series about matrices. Now I have a good understanding. Your videos are so good. No unwanted things. Just straight to the business and that's how I like it. You're giving a lot of knowledge within a short time. So students like us have more time to learn new things rather than wasting a lot of time into a one subject. You're a genius and a life saver. Look I know you're very busy. But still you make videos. That's really impressive professor. You have my full respect... 😁

[@MichelvanBiezen]

Thank you. It is comments like yours that keep us going. It is indeed a lot of work, but as long as students are helped by the videos, we'll keep going, God willing. 🙂

[@mingfeng6963]

I watched all videos you did about matrix. These videos are very helpful for students learning. I am a father of my daughter. I learned much more matrix knowledge from you. I also taught my daughter matrix. Your classes for matrix is very clear and easy to understanding. Thank you so much. You are a super good math teacher.

[@MichelvanBiezen]

Glad you found our videos and you found them helpful. 🙂

[@joshuaonuko]

Thank you King. This made me understand what I could not understand for a week in 3minutes❤

[@MichelvanBiezen]

Glad you found our videos and you found them helpful. 🙂

[@torolfchess7535]

Thank you so much!!!! Beautifully straight-forward & your handwriting's not exactly a disaster like most of us when we use white boards hahah Thanks again sir

[@MahdisFatimaMehdi]

Watched almost 4 videos before watching yours. You are the first one who made it so easy. Thank you so much Sir!

[@MichelvanBiezen]

Glad you found our videos. 🙂

[@kingarthur1077]

you are a blessing first time ever i understand this crammers rule .i blame my lecture

[@MichelvanBiezen]

Hey, that is great!

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[@MichelvanBiezen]

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[@MichelvanBiezen]

Thank you. Glad you like our videos. 🙂

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Wooow...Amazing teacher....Good work sir🎉🎉🎉

[@MichelvanBiezen]

Thank you. Glad you found our videos. 🙂

[@ariefrachman4604]

Sirrr, thank you so much for your educational video. It's very easy to understand for me with not mathematic background. Thank you so much!

[@MichelvanBiezen]

Great! Glad you found our videos. 🙂

[@ariefrachman4604]

@@MichelvanBiezen yes, i was planning to watch some more of your videos to deepen my math knowledge. 😁

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[@MichelvanBiezen]

Thank you. Glad you find our videos helpful. 🙂

[@sheldonblackwood2117]

Very Good video and your way of explanation is very good.

[@MichelvanBiezen]

Thank you.

[@MLBIpa3032]

Thank you for this, this clip helped me understand what I could not for 3 weeks!

[@rinnisdinie7078]

Nice explanation. I could understand easily. Thank you so much sir

[@MichelvanBiezen]

Thanks for the comment. 🙂

[@richardandersen_]

so good la this man, thank you it is easier when you explain than my teacher

[@MichelvanBiezen]

Glad to hear that!

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Thank you so much Sir, very kind of you :') Have my test tomorrow and now I'll be able to do well. Regards💐

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One of the great sir in the world

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Hello from the future. Did you ace your test?

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Great video, watched the entire playlist only wish there were eigenvalues and eigenvectors in this. Your explanations are so easy to understand. Thank you!

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I wish i had a maths teacher like you.. thankyou

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In Arabic we have a famous verse of poetry said : قم للمعلم وأكفه تبجيلا كاد المعلم أن يكون رسولا Stand up for the teacher and give him veneration Because the teacher is almost a messenger ( prophet) Professor Biezen , really you deserve this verse.

[@MichelvanBiezen]

Jamal, Thank you. We really appreciate it.

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Thanks. I have understood well all concepts

[@MichelvanBiezen]

Glad to hear that

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Thank you sir!! you've made these concepts easy to grasp

[@MichelvanBiezen]

You are welcome. Glad you like the videos

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Thanks sir , only because of you i understand this type of sum

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Thank you I understand it fully now, you made it very simple to understand 🙌🏾

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[@MichelvanBiezen]

Thank you. Glad you found our videos! 🙂

[@GlowupwithAno]

Awesome ur teaching way I like this.. M thanku soo much for making me this question easy for me. Thanks a lot...... 😍

[@MichelvanBiezen]

It's our pleasure

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terrific work professor! much appreciated 🤍

[@MichelvanBiezen]

Glad you liked it!

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you always pull through, your're the man.

[@MichelvanBiezen]

We are glad these are helping.

[@nehamariah9541]

Will the signs always be plus then minus and then plus? thanks so much

[@MichelvanBiezen]

Yes, that is correct.

[@heso9828]

Wow i can’t than you enough. Sir you just save my college life! Thank you God bless

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👏👏👏 well done 🥰 thanks alot 🙏

[@MichelvanBiezen]

Thank you. Glad you found it helpful. 🙂

[@ernestbeckham2921]

Thank you professor 💖💖.

[@MichelvanBiezen]

Welcome!

[@cynch831]

Thank you a lot,, understood it one go ...

[@MichelvanBiezen]

Glad it helped

[@Philosjutsu]

1:30 Why are you just changing the signs here? Why was this not explained?

[@MichelvanBiezen]

Good question. That is by definition of the determinant or for cross products of a matrix. But I never looked into why that is so.

[@EzcanSofu]

The universe of linear algebra is extremely beautiful.

[@wardanaeem3803]

Thankyou you almost bald man with a red bow!!!! Saved my poor brain from thinking too much!!!!!😁😁

[@MichelvanBiezen]

Glad I could help!

[@rayanadam4762]

Thank U Teacher 100%👍before this clip i didn´t know how to solve mtrces 3×3 but now😊 i can solve it very well

[@MichelvanBiezen]

Happy to help

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Thank You very much, this video was definitely beneficial

[@johnbrennan3372]

Very clear and easy to follow

[@katemackenzie7119]

Thank you soooo much, I am not going to fail anymore!

[@MichelvanBiezen]

Keep working hard.

[@akankshasharma1178]

Thnkew sir.finally I come to knw that ..how to solve equation by Cramer's rule😊

[@Jaheemjb]

Isn’t it supposed to be times -3 for the matrix 2 ??

[@MichelvanBiezen]

Not sure which matrix you are referring to, but the answers in the video are correct. (You can always check by substituting the final answers back into the 3 equations and see if they match.)

[@beytulk]

Thank you sir :) And happy teachers day

[@MichelvanBiezen]

Thank you

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Thanks you sir. Help for My Advance Studies

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This is so understandable

[@MichelvanBiezen]

Glad you like it.

[@meeraanil382]

Thanks a billion sir !

[@MichelvanBiezen]

You are welcome!

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[@MichelvanBiezen]

Glad you found our videos and that they were helpful. 🙂

[@stories7308]

Easy to understand... thank you Sir 👍

[@anjalikrishna8667]

Thank you so much .... So clearly I understood

[@MichelvanBiezen]

Glad to hear that

[@superdahoho]

PREcalculus? I'm learning this in my linear algebra class which is 3 semesters after calculus :O

[@MichelvanBiezen]

Yes, this is covered in pre-calculus and in linear algebra. Note there are a number of linear algebra playlists on this in this channel that go into much more detail.

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superdahoho which facult you are in civil or computer science

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[@MichelvanBiezen]

Are there specific cases that are not clear to you yet?

[@saraf8356]

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Sir you made it easier

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[@ibrahimaudu4437]

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[@magdalenebassey1268]

Thank you so much🎉🎉

[@MichelvanBiezen]

You’re welcome 😊

[@AkosSam]

Isn't it better to find the determininant using the row that has a 0 in it to simplify the calculations we have to do? P.S. I really appreciate the work you do, you are awsome!!!

[@MichelvanBiezen]

Yes, you can make the job easier by taking a different row. Try it and see if you get the same answer.

[@mezbahuddinevan9490]

well explained sir. Thank you

[@MohitSamantarayIS-]

Sir you can calculate from bottom It is easy to find

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Moja chief 🔥

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That's amazing. Thanks a bunch!

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Mukuru muri chibaba 👊

[@MichelvanBiezen]

Thank you. 🙂

[@saurabhraj2027]

Sir, what if the RHS of linear equation is 0?

[@MichelvanBiezen]

You can solve it the same way. If the equations are consistent it makes no difference.

[@saurabhraj2027]

@@MichelvanBiezen but when replacing them with say X the result of Det(X) becomes 0 ..

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Great video ,thanks

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Thank you very much my amazing teacher

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Thank you so much sir ❤

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Thanks..you sir❤

[@MichelvanBiezen]

You are welcome. 🙂

[@Kodecco]

this helped a lot thank you

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Well done

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its nice dear

[@MichelvanBiezen]

Thank you 😊

[@reineriocagatin1359]

Mabuang nko bayotttt!!!! Ahahaha!! Lord tabang

[@kurigohan1010]

Sir, there is an error with your thumbnail, the answer to Dz should be -14, and not 14 Great video by the way :D

[@MichelvanBiezen]

Thank you for letting us know.

[@yolandetheresa7146]

THANK YOU SOOOO MUCH !!!

[@MichelvanBiezen]

You're welcome! Glad it was helpful. 🙂

[@alimarwat3364]

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[@MichelvanBiezen]

We appreciate the comment.

[@sufyanali7108]

Why u doesn't change the sign of _5 in determinant??

[@olorunseunenoch4175]

Is it only plus minus plus

[@MichelvanBiezen]

yes

[@ashnagurung3406]

Thnq so much sir

[@MichelvanBiezen]

Most welcome

[@xpattv]

So much Respect!

[@gayaniwithanagamage4356]

Thank You..

[@MichelvanBiezen]

You're welcome

[@Dixbe89]

Genuinely don't get how you got to 3 from "2 times, one minus the minus 2 which is a 3"......It has thrown me off because I can not work out how to get close to 3.....

[@MichelvanBiezen]

Can you let me know at what time in the video you have this question?

[@MichelvanBiezen]

I think I understand the question now, "2 times one, minus a negative 2" = 2(1) - (-2) = 3

[@askroni3284]

helpful method

[@thomastse503]

will you make a series about properties of matrices and determinants?

[@miajanepenas7013]

Thank you sir ❗

[@harrisonchimera2129]

Sir. It's not clear on board

[@MichelvanBiezen]

We just checked the video and it appears clear to us. (there are setting that allow you to change the resolution)

[@lilybett9313]

Thanks alot.

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big thanks

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Amazing

[@MichelvanBiezen]

Thanks

[@aldrinkukukri9410]

thank so so so much

[@MichelvanBiezen]

You are welcome. Glad it was helpful. 🙂

thanks you so much.

[@neshofficialgaming5539]

Clear sir

[@MichelvanBiezen]

Glad it helped.

[@Robert1917]

Got it!! Thanx!!!

[@MichelvanBiezen]

You're welcome!

[@arafahmed7180]

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[@prashanttoppo5670]

well explained (Y)