Evaluating the Determinant of a Matrix

When it comes to matrices, beyond addition, subtraction, and multiplication, we have to learn how to evaluate something called a determinant. This is a new concept that only applies to square matrices, so let's learn what it means and how to do it!

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[katiepickrel]

if you all are are looking for a quicker way, you can put your matrix in upper triangular form and take the product of the diagonal of your square matrix. (e.g. make sure all your entries under the diagonal are zero and then multiply all your diagonal entries=det of matrix.) Its way easier for larger matrices.

[emlmm]

Oh man, I'd love full courses in algebra and linear algebra from you. I have a feeling that your exposition of Galois groups and multilinear forms would be legendary. Great work, as usual.

[eldersprig]

What's a permanent? Actually, *what* is a determinant? yeah, I know its *area*, but I don't know what it really means or what you do with it.

[enat]

Literally saving my life!! Thank you so much, explained and shown so beautifully it's actually so hard to believe! Can you pls cover linear independence/dependence and singular matrix decomposition? Thank you!!

[shaz-z]

Why is while we calculate the determinant, we take a subtraction first and then addition?

[jaclynrosenthal]

In what cases do we need to solve for the determinant? In other words, what are some examples of reasons as to why we do this?

[jenm]

Hey professor Dave, thank you for the videos. I keep getting -320 rather than -338 since I’m getting -3 for the efgijkmno 3x3 matrix and subsequently getting +18 rather than -18 for the d portion of the determinant of the last 4x4 matrix question. I’m not sure what I’m doing wrong

[randymartin]

Thank you this is the best series on matrices. I went through 3Blue1Brown's series on linear algebra and his was a bit too much on the graphics and not enough on the computational. He even says he does not do the calculations because a computer can do that for you. The whole point is how to compute manually so you understand from the ground up.

[_WubbleU]

I very much appreciate this. Thank you!

[saththiyambharathiyan]

For 2x2 matrix i understand.... it comes from solving of 2 variables linear equations by elimination of one variable.... But what is the intuition in the calculation of determinat of 3×3 matrix .... Why it is calculated in this method...? When I try to same elimination of variable method... I didn't get the same result.... Could you explain...?

[ahhhhhhhhhhhh]

Thanks, was trying to program n by n matrix determinant calculator. ^^

[beaugalbraith]

So in practical terms what does the determinant tell us? What do matrices with the same determinant value have in common?

[awesomecraftstudio]

Can anyone recomend good ressources on why this works?

[abdullahn]

I like how he goes straight to the point without bullshit

[hansisbrucker]

I really miss the why in this picture 😳

[emangthuso]

Why do you SUBTRACT the product of the second entry from the first row, which is two, and the determinant of the two by two matrix and instead ADD for the next one?

[Tausif-nx]

Love you professor. You're doing a great work❤❤

[debilista]

MY PROFESSORS SUCK SO BAD they do not know this method it appears
I learned most maths in english because in any other language the resources are too scarce or too low quality for effective learning, not even my professors it seems try to find any other methods. Nobody here speaks english? Its first world after all, for real? While others suffer finding and learning from local trash resources wasting half of their lives i can just turn the thing on and pass the semester that easy. 5 minutes of this channel explained more than 2 lectures of local fat professors. The easiest way of finding determinants, unlike professors that encounter unnecessarily huge strings of numbers at 5x5 matrices. So much free time for games, youtube and cola remains at my disposal. Unbelivable.

[veerrajuannamdevula]

Sir why don't we define an angle in terms of line or line segment why only rays?why anti clock wise measure is positive and vice versa? Is it a convention that we follow in maths?

[jds]

ill take your word for it that the product is -338 lolol