[Linear Algebra] Properties of Determinants

When a matrix A can be row reduced to a matrix B, we need some method to keep track of the determinant. I teach the properties in this video that allow us to keep track of determinants as we perform elementary row operations.

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#LinearAlgebra #Algebra #UniversityMath #Lecture

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[tybo]

My professor provided me with a 15 minute minute video discussing the theorems with no examples. This helped immensely, thank you.

[airejtashfeen]

Thanks mate, you saved my mid term at the eleventh hour!

[krissybakes]

first there minutes was extremely helpful! thank you!

[komatsushumpei]

Fantastic, thank you so so much. It really helped me understanding.

[abdultabel]

This was a huge help to study for my exam, thank you.

[heatherlovesyou]

This was kind of confusing because you did not explain why you were doing each step when you switched and multiplied rows.

[Jolopy]

Awesome vid, right down to the core properties

[matrixate]

For the completely clueless, detB is the final result you're looking for. So, in simple english, whatever operations you apply to detA, you need to apply the opposite operations to your result. Some people are taught to do the opposite operations at the very end...it depends on the instructor and book used for the class. In those cases you write the opposite operations on the side of your paper. In this case, he's just placing them to the left of the actual matrix he's working with at every instance he applies an operation.

[akhtarzaman]

Would you please be able to show the proof in 9.31 for the second property please if possible.

[krissybakes]

can you explain why you changed the -1 in the Botton row to 1?

[suhaybyousif]

I'm not sure if your proof for det(A) = det(A') is correct as you're only considering upper triangular matrices, versus considering general matrices. Don't you have to show it must hold for any matrices?

[miguelvargas]

how did you get the -18 and the 12 3:52

[ohyoucanread]

Great video ! You accidentally switched -1 to one though so the det B is 18 not -18

[Amjxad]

6:00 why wouldn't it work if we add R2 + R3 and put it in R3 directly ??

[alicenguyen]

Why did u change -1 to 1 at 5:55? If it’s -1, the det would be 18. But we know that -18!is actually the correct answer. Can you explain this, please?