Linear Algebra 1.1.2 Solve Systems of Linear Equations in Augmented Matrices Using Row Operations

[superioritymelee]

I thought something was wrong with me as everyone else just breezes through these in my class but it was all about no one tried to explain it this way. I just couldn't make the connection between what we are doing and what we actually try to achieve by the row operations. I understand it much better now. Thank you for the great content!

[mbulelogumede]

Kimberly, you're my best teacher so far in linear algebra.

[j.j.]

Thank you for these videos. :) I was trying to do the freecodecamp Linear Algebra class (in preparation for my actual class this semester) and the professor said he was going to explain everything, but then kept saying, "everyone knows how to do this" seemingly every 3 minutes and then not actually explaining things. Your videos are much clearer.

[afgaesthetics]

I was absent the whole semester and tomorrow i have a linear Algebra final exam, your linear Algebra lessons saved me, thank you

[azucenarebolloso]

I'm sure i speak for everyone when I say I wish you were my professor for all my math classes! As a math major, I get upset that a lot of these professors always say, "you should know this already" instead of teaching it in class to make sure everyone is on the same page.

[simpleandminimalmaybe]

i passed my discreet maths because of your course. thank you, once the money starts rolling in i will send a special $Thanks$

[bleachonacob]

One of the best teachers of Youtube University!

[faresobaid]

4:41 it's makes my laugh . I'm the one who make this video lol ... thanks any way

[marianagastelum]

I think you made a mistake in notation @14:20, you took half of your row 1 to be your new row 1 but you put row 2 in the notation (1/2R1-->R2 instead of 1/2R1-->R1). Also, thank you so much for these videos! I really appreciate the extra help! :D

[donovanrao]

The Professor Leonard of linear algebra! (Anyone studying pre-calc -> calc 3 needs Professor Leonard, he is the reason I love math so much, I made A's all the way through calc 3, thank me later!)

[TumeloCarson]

Thank you for this video! All the other videos I watched prior to this one didn't explain why we were manipulating the matrix to achieve 1s and 0s, they assumed we knew why- which was frustrating.

[aboodhoms]

the answers are ( -1, 0, -1) you have missed the -4 when you multiply it by 2, it is -8 not 8. correct me if im wrong thx.

[halowiz]

These are incredible videos, being an engineering student taking pre-professional courses I have found myself behind in my linear class. So thank you, truly for your work. I did have a question about the Replacement part of Row Operations. You had put -2R2 + R1 = R2. Should it have been -2R2 + R1 = R1? This was at 1:23 in the video. Thank you again.

[gerardtavares]

This is a good math to practice during the summer 😊 thanks for the video

[chimdiebubeokoro]

20:07 Instead of Row 2 - Row 3 to be the new Row 3, I did half of Row 1 + Row 3 to be the new Row 3 and at 20:43 instead of a third of Row 3 to be the new Row 3, I did -2 multiplied by Row 3 to be the new Row 3.
In the end, my solution was (22, 12, 2) but the main matrix was the same as yours and all my other steps were the same. What did I do wrong please?

[quinquintero]

Is scaling the only method in which we multiply the constant to the value (right side of augmented matrix)?

[rd]

At 3:18, your equations and the matrix don't match up for row 3. You have to change the 3rd equation to -> -4x, 1 + 5x, 2 +9x, 3 = -9. Otherwise, when you substitute the points (x, y, z) -> (29, 16, 3) back in, it won't make sense.

[altheebqatar]

In the pr ties question why did u make the the number above the rectangle 0 is it nessary ?

[davidmurphy]

I'm struggling to picture the replacement row operation geometrically. I'm interpreting the matrix as a row basis which we're looking to transform into an orthonormal identity matrix basis.

So we've got a vector plotted with the starting weird arbitrary basis. So we want to see where that vector lands plotted on standard x, y z unit vectors.

So scaling a row is obviously valid as long as you replot the vector. Swapping rows doesn't change the space, it's just a change in our representation of it. Ie a rotation.

Now substitution is obviously an operation on a R2 plane within R3.

But it's not clear to me why this preserves the latent space...

Oh wait, it's a shear! You're just straightening it up so it's at right angles. Right, got it.

Rotation, scale and shear on a row basis matrix to make it an orthonormal basis matrix. And then you just shift the vector along with it.

Really, you should have said that. It's confusing just doing the operation without knowing why.

[_atif_]

shouldnt the coefficient of X3 at R3 be -5 at 20:32 and not -3?