- Видео 98
- Просмотров 6 379
Dylan ArceJaeger
США
Добавлен 12 дек 2011
Week 4 | Lesson 18 | The Determinant
0:00 Intro
0:38 2x2 determinant (how to do it)
2:33 3x3 determinant (how to do it)
4:23 When can you take a determinant?
4:49 General form to calculate determinant along the first row
9:59 We can actually expand upon any column or row!
11:05 Example of 3x3 determinant along the first row and then the first column
16:06 Triangular matrix (definition)
18:14 Determinant of triangular matrices (special theorem)
19:14 Example demonstrating the power of the theorem
20:41 What happens to the determinant if you do row operations? (theorem)
23:30 Example row reducing to Echelon form to use the determinant
28:20 General notation for calculating the determinant by expanding on any row/column
30:07 Cofactors (def...
0:38 2x2 determinant (how to do it)
2:33 3x3 determinant (how to do it)
4:23 When can you take a determinant?
4:49 General form to calculate determinant along the first row
9:59 We can actually expand upon any column or row!
11:05 Example of 3x3 determinant along the first row and then the first column
16:06 Triangular matrix (definition)
18:14 Determinant of triangular matrices (special theorem)
19:14 Example demonstrating the power of the theorem
20:41 What happens to the determinant if you do row operations? (theorem)
23:30 Example row reducing to Echelon form to use the determinant
28:20 General notation for calculating the determinant by expanding on any row/column
30:07 Cofactors (def...
Просмотров: 91
Видео
Week 4 | Lesson 17 | The Invertible Matrix Theorem
Просмотров 4816 часов назад
0:00 THIS VIDEO IS VERY IMPORTANT 1:37 What can we infer is the columns of A form a linearly independent set? 10:18 Invertibility from one-to-one and onto
Week 4 | Lesson 15 | Matrix operations
Просмотров 11516 часов назад
0:00 Intro 1:04 Matrix multiplication 5:15 Matrix multiplication is NOT commutative 9:08 Matrix addition 10:47 AB = 0 doesn't imply A or B = 0 12:32 Example where AB = 0 but A and B are not the 0 matrix 13:41 Matrix exponents 16:05 Matrix division does not exist 17:50 Matrix transpose 21:34 Transpose theorems
Week 4 | Lesson 16 | Matrix Inverses
Просмотров 4716 часов назад
0:00 Intro idea 0:31 Matrix inverse (definition) 2:47 2x2 matrix inverse 3:47 Using the inverse to solve a matrix equation 9:58 Matrix inverse as a transformation inverse (visuals) 11:51 Figuring out the inverse of larger matrices 13:15 Example finding 3x3 inverse
Week 3 | Extra | Intro to thinking theoretically
Просмотров 11221 час назад
Week 3 | Extra | Intro to thinking theoretically
Week 3 | Lesson 14 | One to one and onto transformations
Просмотров 68День назад
0:00 Intro 1:23 One-to-one transformation (definition) 2:44 How does one-to-one relate to solving Ax=b? 3:36 Visual explanation for one-to-one 9:09 Back to solving Ax = b and one-to-one 10:41 Onto transformation (definition) 12:22 Visual explanation for onto 17:11 How does onto relate to solving Ax=b? 19:18 Theorem (relating onto and Span) 22:09 Theorem (relating one-to-one and linear independe...
Week 3 | Lesson 13 | Contractions, dilations, and rotations
Просмотров 52День назад
0:00 Intro 1:00 Contraction & Dilation transformations 1:18 The Identity matrix (loose definition) 3:19 Rotation transformations (example) 7:54 Rotation transformations (harder example)
Week 3 | Lesson 12 | Linear Transformations (for real this time)
Просмотров 117День назад
0:00 Intro 0:52 Linear transformation (definition) 2:12 Where have we used the property of linearity before? 4:49 Example proving a transformation is linear 19:25 How do we create the standard matrix A for the transformation? 20:29 Standard basis vectors (loose definition) 22:39 Creating the standard matrix A. 24:43 Why does the theory work? 28:26 Example creating a standard matrix for a linear...
Week 3 | Lesson 11 | Linear Transformations (theory)
Просмотров 110День назад
This video is a premise for Linear Transformations. However, the entire video I only talk about a general transformation and not the specifics of a Linear Transformation. Misleading title, I know. 0:00 We made it to the theory 0:34 Remembering how functions work 1:21 Codomain vs Range 2:42 An example of codomain vs range 5:31 Mapping from one space to an entirely different space 10:13 Transform...
Week 3 | Lesson 10 | Applications of Systems of Equations
Просмотров 64День назад
0:00 Back to systems of equations 1:21 Application 1 | Economics 10:39 Application 2 | Chemistry 26:38 Application 3 | Network flow
Week 2 | Lesson 9 | Homogeneous vs. nonhomogeneous systems and describing solutions sets
Просмотров 10721 день назад
0:00 Sorry not sorry 0:42 Homogeneous system of equations (definition) 1:21 Example 3:08 How to describe a solution set 5:56 Writing a solution set using vector notation 7:45 Free variables correspond to spanning of vectors! 9:08 The solution set can be described by spanning vector(s)! 11:33 Example (describing solution sets using vector notation and span) 16:30 Example (nonhomogeneous system o...
Week 2 | Lesson 8 | Relating systems of equations, vector equations, and matrix equations
Просмотров 7521 день назад
I HAVE AN ERROR IN THE VIDEO AT 15:33 WHERE I DON'T WRITE OUT THE WORD "EQUATION" AFTER "MATRIX." I SAY IT OUT LOUD BUT FORGOT TO WRITE IT!!! 0:00 Premise 0:55 Matrix multiplication (brief definition) 2:34 An example 6:26 An example relating a system of equations, vector equation, and matrix equation 15:33 Matrix equation (definition) there's a small error here (see start of summary) 20:21 Glea...
Week 2 | Lesson 7 | Solving vector equations
Просмотров 8621 день назад
0:00 Intro 1:07 What are we doing in this video? 1:45 What does it mean to be in the span of some vectors? 2:55 Vector equation (definition) 3:34 Big idea to answer questions about span 4:41 Doing the algebra 12:45 IMPORTANT System of equations vs. vector equations
Week 2 | Lesson 6 | Vectors (theory)
Просмотров 9121 день назад
0:00 Going in a different direction 0:39 General vectors in this class 1:30 Linear combination (definition) 3:39 Linear combination of one vector (visual aid) 6:06 Span (brief mention) 7:08 Linear combination of two vectors (visual aid) 10:58 The lattice diagram (visual representation of the span of two vectors) 14:40 Span (definition) 16:02 Span of one vector (visual aid) 17:13 Span of the zer...
How to solve WAMAP problems
Просмотров 4028 дней назад
0:00 How is Linear Algebra different from other math? 0:54 How to answer T/F problems 4:01 How to answer algebraic problems 6:00 A warning 7:48 What to do if you get a T/F problem wrong
Week 1 | Lesson 5 | Interpreting matrices (for solutions)
Просмотров 81Месяц назад
Week 1 | Lesson 5 | Interpreting matrices (for solutions)
Week 1 | Lesson 4 | Recapping matrices
Просмотров 47Месяц назад
Week 1 | Lesson 4 | Recapping matrices
Week 1 | Lesson 3 | What do we need to know about matrices?
Просмотров 71Месяц назад
Week 1 | Lesson 3 | What do we need to know about matrices?
Week 1 | Lesson 1 | Linear Systems of Equations
Просмотров 100Месяц назад
Week 1 | Lesson 1 | Linear Systems of Equations
Integration by Parts: The Table Method
Просмотров 153 месяца назад
Integration by Parts: The Table Method
Week 5 | Extra | Even and Odd Functions
Просмотров 368 месяцев назад
Week 5 | Extra | Even and Odd Functions
Great video but the symbol ∈ is definitly not an epsilon
You are entirely correct! I definitely misspoke--that symbol actually doesn't even have a name, as far as I can find on the good ol' interwebs...!
Cool
Glad you think you!
'Promosm'
Sorry, I don't understand your comment.
In your country which grade have you began to study this ? As a vietnamese student, i have studied this since grade 11 🥲
Hi there, It depends on the school and student. I would say grade 8 or 9 is when most learn about trig functions (in Geometry class) and then about grade 10 or 11 they dive deeper into them (in Precalculus/Trigonometry class).
When you were going over describing elliptical regions using polar coordinates, I think the minor y-axis should be 2 not 3 since the y portion of the function is y^2/4.
You are absolutely correct! I will figure out how to modify the video to say that. Nice catch!
16:29 you just gave the Terminal point. Then stated you gave us the terminal point with no justification. Then proceeded to give no explanation. You showed how to fact check the answer, but Im not figuring out how you got that answer in the first place. I followed along on the first example with both X and Y values having to be the same.
Hi there, You are correct--I gave this particular point with no justification, other than giving the slight verification that at the very least they are values that happen to work with a right triangle. The proof of this is not something I immediately cover in my class. The reason is twofold: First, it's more useful for my students to (in the moment) go with the flow and start working with the larger concepts instead of wondering how exactly every single terminal point at every possible angle could be proven. Second, the proof is very easy and I assign it as homework for my students. If you'd like to try proving the terminal point yourself, try drawing an equilateral triangle with side lengths of 1 and then cut it perfectly in half. What can you say about the angles in your two half triangles? What about their side lengths? Hope that helps!
got my sub
Thank you for the video!
Okay Dylan I see you Mr. RUclips TA
I'll remember you when I'm rich and famous.
Great video!
Appreciate it! Share with all of your lost math friends :D