Linear Algebra 4.3.1 Linearly Independent Sets and Bases

[jacobzweifach]

@12:33 it should be a negative 4 not a positive 4. Not a big deal, just pointing it out. Thank you again for making these videos Ms. Brehm. I watch them before my professor lectures on the topic.

[abdullaharean]

I really understood Linear Algebra and felt the inner things through your incredible lecture series. I don't know if you will read my comment or not but I really appreciate your effort and Love from Bangladesh!

[livinlifewithlola]

ugh i need you to explain change of basis cause i genuinely cant understand from anyone else but you. you make it so simple and easy to understand

[unbendedurchin]

Respect, almost done with spring break and I went from 0 understanding to almost 80 percent. Humility is a great thing, we have a test on chapter 3-5 in two weeks

[qenxnwh]

the best explanation for linear algebra respect from China

[ilkokul-karnesi]

STANDART BASIS : "Base of basis". WOWW ! Thanks for this definition ♥

[averysnyder]

Love your videos! Thank you for all the examples you give and going over previous concepts. I love it when teachers know that I need a refresher on previous concepts learned because you best believe I have forgotten then after the test.

[xoppa]

A set of vectors {u1, u2, ... up} are linearly independent if the nullspace of the matrix A = [ u1, u2, ... up ] is just the zero vector.

[moochris]

@11:26. what do you mean by not a subspace? Does a basis only works for a square matrix? Because both vectors have 3 entries, they must also span R3 which is 3 vectors? I thought they have to be linearly independent which they can be because there are pivots in every column.

[anonymous]

In the basis example @10:45, it could span for R2, as the rank of the matrix was reduced to R2 in its reduced echelon form. Am I right?

[waterfall-rn]

Hii How can we say that it’s linearly dependent if they are a linear combination this is not always true since sometimes they can be linearly independent and are linearly combined (forming a basis)

[donzywenx]

Hii Brehm! Your videos are really helping me for my exam I have in 5 days. I want to ask, can we call a set linearly independent if their determinant is not equal to zero?

[kagisogodbe]

v2 shows -4 but you wrote it as 4 only, affecting resultant, becomig 15 instead of 2(-4)=1

[sayanbaidya]

isnt determinant / rank more efficient to find indepent condition

[avielb]

15:48
Shouldn’t the there be only 4 basis vectors for P^4? Why are there 5?

[santoszuniga]

why is the p written like that? does it stand for something?

[abdullahfarooq]

@9:10 it should be linearly independent ?

[tidalfriction]

At 6:00, why did you choose to subtract from row 1 using row 2 as opposed to Row 3? Was it just choice?

[serafic-kj]

anyone can please tell me where to find the solution this Linear Algebra 10 edition?