Solving a 3 x 3 System of Equations Using the Inverse

[theanamex]

way more useful than my 2-hour lecture on the topic. Thank you so much, it really made me understand.

[njitram]

To anyone wanting a practical use for this, I just used it in real life :-)

I'm buying a house and am calculating how much I actually get to spend on the house when taking a loan.
I have 3 variables: Notary costs, taxes and how much of the loan I can spend on the house after the costs have been subtracted. The taxes and the notary costs are dependant upon the price of the house in a pretty complicated way (Belgian law...)
I reduced it down to a system of 3 equations. First I tried to solve them on paper using substitution and such but just like on exams, something goes wrong along the way and the end result is completely wrong (3 page full of equations...)

Then I remembered using vectors in class. Excel can't handle systems of equations (circular dependencies error) but it can calculate the inverse matrix and from that I obtained my solutions. Now I have a flexible excel file that will simulate any loan that the bank is willing to give me.

So yes, this stuff can be useful in real life.

[pengzhang]

if u were our professor in university, i would attemp every class everyday. big thumb up for u.

[PeteDork]

I remember watching your videos on my pre-calc class all the time. Just shows how lazy my teacher was

[imbali_janeachy]

Thank u from kenya..this has been giving me problems for weeks now but ur explanation has made me understand...i can now tackle the question easily thanks.

[VeritasOmnias]

I think I would personally leave the 1/25 out front and just multiply the inverse and matrix b. I find multiplying numbers much easier than dealing with fractions. It's just personal taste though. Great video :)

[tristiankinney]

everything was going good until you pulled the second paper out

[YazhShah]

At 4:18 what he did in simple terms is the transpose where you just turn all the rows into columns.

[desmondnathson]

thanks alot man. can you make a video for a 3x3 eigenvector and eigenvalue example?

[desireenaidoo]

Thank you so so much! Your examples are so clear, concise and well explained. You really helped me with Math this semester! :)

[mpanayotov]

Thank you, very detailed explanation, exactly what everyone else failed to do.

[efralopez]

Thanx for posting this man. My teacher goes too fast and skips steps often thinking that we know what hes doing and i was completeley lost but now im starting to understand it. Thanx again

[ataokilo]

learning this during my open book exam during covid. Life saver

[rrfmyc]

Is it just me or the sound of the sharpie on paper makes gives me goosebumps, like fingernails on chalkboards goosebump?

[watsanmathenge]

Thank you so much. I have been having a hard time doing mattrix but after learning from you it look easy

[tankyasfak]

Well done. You explained every step clearly and now thanks to you i am able to understand this topic

[mimigirl]

Dude. every time I look up a mathematical video your videos always appear and it's always the best !!! you've been SAVING ME all through high school and -currently- university YOU'RE THE BEST !!!

[alexandrashvydun]

thank you for including the section where you explain covering up rows and columns to get the determinants

[MayankLongiany]

Another left-handed legend on YouTube! Lefties rule ;)

[arskhan]

Informative and tremendously useful video. Since my professor had demanded that we determine the inverse through transforming to RREF form along with the identity on the right hand side of the augmented matrix, I will be using that method for finding the inverse.