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

[MrPoutsesMple]

A Greek math teacher had taught me the "Russian" method. Pretty neat, and memorable. Nice to know that Russians do it that way as well.

I had tried once to see if there's a similar pattern in a 4x4 determinant, but didn't find one. Do you know if the pattern exists in dimensions d > 3 too?

Thanks !

[briancheung]

This Russian method is described in a very famous book on Linear Algebra by Russian mathematician. See Georgi Shilov Linear Algebra.

[alejandrohazaelsanromanpla]

This method is the same as in México to obtain 3x3 matrix but personally I prefer Montante's method for matrix of more than 3x3 note, the name of the method is "Sarrus" when you understand it, is really easy and quickly

[wallhackio]

Never seen the Russian mneumonic before. Is there a name for it? I can't find any other resource that describes what is shown here.

[StewieGriffin]

american way is alternating addition and subtraction from Row 1's terms
1(5*9 - 6*8) - 2(4*9 - 6*7) + 3(4*8 - 5*7)

The Russian way makes you find the determinant mentally without writing anything down.
Just look at the matrix and do some mental calculations and done
Also note that the terms you see are all unique. All numbers 1-9 shows up once (simply count from 1 to 9 looking at each row in the video)

We know that if (a + b + c) - (d + e + f) = (a - d) + (b - e) + (c - f)
if a = 1*5*9 like in the video then just substitute the equation in the video with the letters in my equation
Practice it and you can find the determinant for any 3x3 matrix
4x4 matrix is literally easy.You find the determinant of the 3 inner 3x3 matrices Then just multiply the term # with the matrix determinant (This is the American Way)

[dsfgoppudfgihdsf]

what are with all the soccer images? lol love it!

[ektabansal]

Professor seems to be a big fan of messi