Determinants of Triangular Matrices | Linear Algebra

We discuss how to find the determinant of triangular matrices of any size. This includes determinants of upper triangular matrices, determinants of lower triangular matrices, and determinants of diagonal matrices. We see through a generalized example of the cofactor expansion that to calculate the determinant of a triangular matrix, we need only multiply the entries in the main diagonal. #linearalgebra
Minors and Cofactors: • Minors and Cofactors o...
Cofactor Expansion of the Determinant: • The Cofactor Definitio...
Linear Algebra course: • Linear Algebra
Linear Algebra exercises: • Linear Algebra Exercises
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[@WrathofMath]

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[@onwritersbehalf]

I am Economics student and your videos helps a lot. Our whole class sees your videos and it helps us a lot so thankyou very much.

[@WrathofMath]

Glad to hear that! Thanks for watching!

[@PunmasterSTP]

How are your econ classes going?

[@alexkotusenko302]

thank you

[@pipertripp]

So is the proof of the theorem done using induction? Something like "we'll if the determinant of a generic k x k matrix is the product of the diagonal elements then we can show that a k+1 x k + 1 matrix is also the product of diagonal terms" or thereabouts?

[@WrathofMath]

That's correct, since in that induction step the determinant of the k+1 by k+1 matrix is just the first diagonal entry times the determinant of the first minor, which is the determinant of a kxk matrix.

[@DarrelShokane]

Thank you for your videos😭💥

[@WrathofMath]

Thanks for watching!

[@dhritysarmah9762]

Can you make a video on how to Vectorize a square matrix

[@krishvardhanmaini2301]

Thank you for the video.

[@WrathofMath]

Thanks for watching!

[@oscarlaruta2008]

In both case , which want is not a vector space, and why?

[@PunmasterSTP]

Those types of matrices are definitely...triangulawesome! 👍📐