Simpler 4x4 determinant | Matrix transformations | Linear Algebra | Khan Academy

Calculating a 4x4 determinant by putting in in upper triangular form first.

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[danholocaust]

Youtube is a better friend than teaching books!

[taekwonwelchify]

its 12:30 am, i got my test at 8 am, and i COULD NOT figure out where those negative's (from swapping rows) were coming from... id be doomed without this video, thank you!!!

[philipgao]

What if you interchange rows more than two times? Does that mean every time you swap two rows you get a negative sign?

[EngineerPrepper]

Perfect explanation, precise and to the point.. .Great Job!

[INC]

I LOVE YOU SO MUCH! Why is this incredibly simple method not taught in maths lectures?

[Beskhuepnm]

You could try to get the matrix into a form where only 1 row starts with a non-zero number. Then, you calculate the dertiminant of this new matrix, which is just a constant times the determinant of the 3x3 matrix you get, which is pretty easy to calculate.

[niFeforever]

Well this method is only useful with matrices which were intentionally made to be easily solvable, I mean good luck using this method in this 4x4 (54, 46, -85, 156), (-23, -2, -121, -69), (-61, 203, 40, -183), (16, 12, 1, 48), the answer is 0 btw.

[murtez]

the great thing is when someone explain difficult idea in simple way in only a few minutes I mean seriously wow 🐸😱this was amazing

[anezkalascakova]

Is it working everywhere, or just on special types? For example, matrix like 1.row (1;2;1;-2), 2.row (0;2;1;2), 3.row (-1:3;1;3) and 4.row (-3;4;3;2), the determinant should be 22, but i cannot get that answer.
Thanks

[waynesaviour]

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[viktorbarsukov]

is that the ultimate question to Life, the Universe and Everything

[Amanijamac]

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[sfkc]

Ah that's what my teacher was talking about. The only words I picked up were triangle, zero and matrix but now I know what to do. Thanks!

[shiningyrlife]

@enjoyablesounds according to him, when u change row, the determinant of the matrix after changing is negative of the determinant of the matrix before changing row. That why u put a minus sign.

[Marauder]

When you flip rows you add a negative, but if you flip some rows again, do you cancel the negative (add another negative)?

[justindza]

This took me a little while but using a row 1 will put a nonzero in the 1st column, 4th row. Which will take away from putting in reduced row echelon

[alialiyev]

u are best teacher. u know this job, man! thank u for explaining.

[mesumabbas]

Thanks it helped.
Next day after tomorrow is my paper.

[enjoyablesounds]

I don't understand why you wrote a minus after the row exchange..If i'm not mistaken you are just old fashioned row reducing right? Or is it a standard rule that when figuring out determinants you must switch signs when exchanging rows?

[sulthananajeeb]

beinging maths studying is well good for studying the matrix study easy to well understanding super experience fot students