Determinant of a 3x3 Matrix

In this video, I showed how to compute the determinant of a 3x3 matrix by first computing the cofactors or otherwise

[punditgi]

I have determined that Prime Newtons is the math channel to watch! 😊

[RaWr-uj]

u r so good at explaining! thank u so much

[kingbeauregard]

Here's a question: what is your interpretation of the meaning of a determinant?

Complicating matters is, I've heard the term used in a couple different contexts. one of them is, in the quadratic formula, the part under the square root is sometimes called the "determinant", and I'm not sure why. I don't get the common concept behind it all.

I have a fondness for determinants though. You can use them to solve systems of linear equations (Cramer's Rule). You can use them to determine if systems of equations are linearly independent.

[dougaugustine]

Here's another video I need to watch again. Sure seems like a lot of opportunities to make silly computational errors!!

[Quincy-fmfu]

hey, thanks for the video, sir. I can understand the calculating process, however, I would like to know why do we do it like this? Any geometric interpretation please?

[shuaibjemil]

Thanks so much sir.
Please sir, kindly help us with "Game Theory"

[holyshit]

Chosen column can be expressed as linear combination of vectors then determinant will be sum of determinants
and in each determinant in that sum chosen column is replaced with that vectors
Here is example
det([[a_{11}, bv_{1}+cw_{1}, a_{13}], [a_{21}, bv_{2}+cw_{2}, a_{23}], [a_{31}, bv_{3}+cw_{3}, a_{33}]]) = b*det([[a_{11}, v_{1}, a_{13}], [a_{21}, v_{2}, a_{23}], [a_{31}, v_{3}, a_{33}]])+c*det([[a_{11}, w_{1}, a_{13}], [a_{21}, w_{2}, a_{23}], [a_{31}, w_{3}, a_{33}]])
This with cofactor expansion can be helpful if we want to expand characteristic polynomial written in the form det(A-λI)