Linear Algebra 14TBD: Calculating the 3x3 Determinant the Indian Way

[charbilrom]

What a video!
Time caught me last week during midterm exam when trying to find the inverse of 3x3 with some weird fractions. I didn't know I was using Indian approach but after this incredible explaination. I will laugh during final exams. Thanks alot. I give you 1k likes, 1k subscribers and 1m views.

[MFMegaZeroX]

As an American, I actually learned the Indian way in high school, interestingly enough. I never saw the "American" one until college.

[holyshit]

In Polish schools this method is connected with Pierre Simon de Laplace
(Laplace expansion of determinant)

[FirstLast-ujud]

Huh, as a Canadian student with a Russian teacher, I learnt the Indian way here in university. Anyway, great explanation, thank you!

[gentlemandude]

It's great to see all these methods side-by side.

[knivesoutcatchdamouse]

I'm American and I learned the 'Indian' approach, but I learned it as the method of Laplacian expansion. However I was taught the equation for the general n×n determinant first along with thr theoretical motivation, so it made perfect sense when it came to the whole cofactors and submatrices aspect.

[randyhelzerman]

I went to high school in Indiana (not India :-) but they still taught me the Indian way of finding the determinant.

[colinskinner]

Not sure that the "Indian" method is Indian at all. I took linear algebra, physics and multi-variable calculus in college in California and in all courses we used the co-factor method ("Indian" method). This is the first time I've seen the "American" method.

[ILikeEpicurus]

Didn't know about Russian or American methods. Seems that here in Europe the Indian method is the preferred choise. Even because it is expanded easy to higher order matices.

[yoavwilliamson]

awesome help very good explanation thank you

[abajabbajew]

Also known as cofactor (Laplace) expansion, this method allows writing down - i.e. representing in a determinant - the vector cross product of two vectors when the three basis vectors occupy the first row and the vector coefficients occupy rows 2 and 3, as well as the signed area of a triangle by (I believe) putting '1's into the first row and the x's and y's down each column - or by putting x's, y's & z's down the columns becomes the triple scalar product which corresponds to the 'volume' of a parallelepiped . (So it's very versatile)

[MrPoutsesMple]

This was the standard method taught in Greek high schools, but I had always trouble remembering the signs. Did they start with a plus or a minus, I've always wondered. The Russian and the American methods seem more reasonable... Thanks again !

[oystercatcher]

Thank you! Seems in the American you can easy just wrap around the diagonals in your head rather than writing it out getting a simple approach with a little more ‘thinking’. But any approach seems easy with a little practice

[RuthvenMurgatroyd]

This is just Laplace or cofactor expansion. This is the most general method but for working with 3×3 I honestly consider it overkill (although it is kind of fun and hypnotic in a way) ans prefer the Rule of Sarrus or what you call the American method.

[acruzp]

So I was taught the "American" approach as "Cramer's Rule" (do not know why since it isn't) for determinants, and this "Indian" method was taught to me for solving cross products and the fact that it is a determinant calculation was omitted. Education huh...

[hyunjeon]

it is similar to crossing two vectors in America, the difference is whether you leave the final answer as a vector or add them together as a scalar

[YuzuruA]

In Brasil, I learned a slight modification of the Russian method.

[ultramadscientist]

Floridian, I've been using the indian method for years apparently

[IvanPagnossin]

It's only for me or this is the only video which does not load?

[nomadr]

Funny, I am about your age, I studied at a school and in the university in the damned former USSR, but never heard of your so-called "russian" approach, always this one... I wonder how comes?