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Drew Werbowski
Приєднався 28 лип 2018
Former TA at University of Waterloo with BASc. Mechanical Engineering
Linear Independence Test in Function Spaces
Let's determine if a set of vectors that belong to a function space is linearly independent!
Переглядів: 41
Відео
How to Determine if a Set of Vectors is Linearly Independent (Easy Explanation)
Переглядів 5121 годину тому
Let's look at the logic behind the linear independence test and why it actually makes sense!
Finding Basis of Kernel and Range of a Linear Transformation - Linear Algebra
Переглядів 12 тис.11 місяців тому
What is a Kernel and Range of a linear transformation? How do we compute these and find their respective basis? This video aims to answer these questions.
How to Find the Intersection of Planes - Linear Algebra
Переглядів 2,7 тис.11 місяців тому
We use Gaussian elimination to solve a system of equations that gives us the equation of a line that represents the intersection between 2 planes.
Shortest Distance Between a Line and a Plane - Linear Algebra
Переглядів 3,4 тис.11 місяців тому
Let's look at what the shortest distance might be between a line and a plane in R3!
How to Find the Shortest Distance from a Point to a Line - Linear Algebra
Переглядів 3,2 тис.11 місяців тому
Finding the shortest distance from a given point to a line given the vector equation. Very common question in MATH 115: Linear Algebra for Engineering at University of Waterloo.
How to Use Squeeze Theorem to Solve a Limit - Calculus 1
Переглядів 32511 місяців тому
We go over a midterm/final level limits question that uses squeeze theorem to solve a limit. Professors will often throw curve balls at you on evaluations to test how well you really understand a concept. This question is great for testing your understanding of inequalities and squeeze theorem.
Limits that Approach Negative Infinity - Calculus 1
Переглядів 37211 місяців тому
We solve the limit of a rational function that approaches negative infinity using 2 approaches. It's easy to get the sign wrong on these questions, so I hope this video clears up this common mistake!
How to Simplify an Equation to a Single General Cosine Function
Переглядів 86Рік тому
We are given an expression with multiple trig functions and asked to simplify it into a general cosine function. This video will make you understand what you are doing and not memorize a process!
How to Simplify an Equation to a Single General Sine Function
Переглядів 169Рік тому
Simplifying an expression with multiple trig functions into a single sine function. It's as easy as using a quick trig identity and solving a system of 2 equations!
How to Solve Inequalities with Absolute Value - Calculus 1
Переглядів 76Рік тому
Absolute values can be hard to understand. I hope this video clears things up with how to approach an ugly question which combines inequalities and absolute values. If you can do this, you can ace your exam!
How to Solve Inequalities with Logarithms - Calculus 1
Переглядів 80Рік тому
In this video we solve an inequality that contains multiple logarithm terms. These questions are more difficult to understand and you must consider the domain of the logarithms as well! Great question to test your understanding of inequalities, logarithms, and how prepared you would be if this were to appear on a midterm or final exam!
Proof by Contradiction Using Rolle's Theorem - Calculus 1 Example
Переглядів 233Рік тому
Proving a function cannot have 2 real roots using Rolle's Theorem and proof by contradiction. Disclaimer: I have an engineering degree, not a math degree. Math majors feel free to nit pick the rigour of this proof!
Rolle's Theorem Easy Explanation and Examples - Calculus 1
Переглядів 52Рік тому
Brief explanation of Rolle's Theorem and how to apply it to a couple examples!
Solids of Revolution - Calculus (Disc and Cylindrical Shell Method)
Переглядів 259Рік тому
In this video, we construct two integrals for the volume of a solid revolved about a horizontal line.
Proving a Transformation is Linear - Linear Algebra
Переглядів 4,5 тис.Рік тому
Proving a Transformation is Linear - Linear Algebra
Subspace Test and Finding Bases for Polynomial and Matrix Vector Spaces
Переглядів 2,5 тис.Рік тому
Subspace Test and Finding Bases for Polynomial and Matrix Vector Spaces
Subspace Test for Intersection, Union, and Sum of Subspaces - Linear Algebra
Переглядів 1,9 тис.Рік тому
Subspace Test for Intersection, Union, and Sum of Subspaces - Linear Algebra
How to Simplify a Span of Vectors - Linear Independence - Linear Algebra
Переглядів 1,5 тис.Рік тому
How to Simplify a Span of Vectors - Linear Independence - Linear Algebra
Markov Chains Detailed Example (Easy Explanation) - Linear Algebra
Переглядів 933Рік тому
Markov Chains Detailed Example (Easy Explanation) - Linear Algebra
How to Approximate Using Differentials - Calculus
Переглядів 271Рік тому
How to Approximate Using Differentials - Calculus
How to Solve Linear Matrix Equations - Linear Algebra
Переглядів 263Рік тому
How to Solve Linear Matrix Equations - Linear Algebra
Proving a Limit Exists with Delta and Epsilon Definition of a Limit
Переглядів 306Рік тому
Proving a Limit Exists with Delta and Epsilon Definition of a Limit
How to Find Complex Roots Using DeMoive's Theorem - Linear Algebra
Переглядів 520Рік тому
How to Find Complex Roots Using DeMoive's Theorem - Linear Algebra
How to Convert a Complex Number from Polar Form to Standard Form - Linear Algebra
Переглядів 1,9 тис.Рік тому
How to Convert a Complex Number from Polar Form to Standard Form - Linear Algebra
How to Convert a Complex Number from Standard Form to Polar Form - Linear Algebra
Переглядів 1,4 тис.Рік тому
How to Convert a Complex Number from Standard Form to Polar Form - Linear Algebra
What is Polar Form of a Complex Number - Linear Algebra
Переглядів 178Рік тому
What is Polar Form of a Complex Number - Linear Algebra
How to Apply Squeeze Theorem - Example - Calculus 1
Переглядів 387Рік тому
How to Apply Squeeze Theorem - Example - Calculus 1
How to Divide Complex Numbers - Linear Algebra
Переглядів 174Рік тому
How to Divide Complex Numbers - Linear Algebra
How to Take the Square Root of Complex Number - Linear Algebra
Переглядів 265Рік тому
How to Take the Square Root of Complex Number - Linear Algebra
babe wake up drew werbowski uploaded again
Good video,but can I ask something. Since the definition of a bases states that not only must the list be linearly independent but must also span the entire vector space. How do we prove that or is it not necessary for this proof?
Yes, you’re right that we need to prove both the vectors are linearly independent and that they span the entire vector space the vectors are a basis for. There are multiple ways to show this and it depends on the question. I believe I have a video on my channel highlighting an example
@@DrewWerbowskiOkay I'll check it out, thanks for this one I learnt a great technique from it.
Hi Drew! I'm Victor. Good video that I totally understood
😂😂😂🥶🥶🥶🥶🥶😮😮😮😮😮🤯🤯🤯
babe wake up drew werbowski just uploaded
Why do you use j instead of i for the imaginary unit?
In engineering some professors use lowercase j to avoid being confused with another parameter such as electrical current
@@DrewWerbowski thanks
You are such an amazing teacher!
bro! You are my hero,It's a pity that I discovered this channel too late, I have an exam this afternoon.
thank you so much.....
So why nulity is 1?
i have a question here basis of kernal is empty then.it has no dimension..means zero dimension.but dimension.of Kernal equals nulity so here we seee nulity is 1
Thanks bro you actually saved me
fantastic job
3 years later and Drew, sir you are amazing. Thank you so much, you are a life saver!!!
Why is it -x(-sin(x)) at 4:01, not -xsin(x)?
Nice, succinct explanation. I just wanted to confirm what an Eigenspace is and this was the perfect video. Didn't need to wade through a 20 minute exposition on all things "Eigen" to get there. Cheers!
Good
Nice. A tip for the future, start off with the most central, interesting and motivating information, namely drawing the shortest distance from point P( 3,3,1), and from the start telling that the closest distance must be a line perpendicular to line L. THEN you construct the vector equations that gives you that sought vector ( the perpendicular one ) and the distance along it from 3,3,1 to the line.
There are unknown way to visualize subspace, or vector spaces. You can stretching the width of the x axis, for example, in the right line of a 3d stereo image, and also get depth, as shown below. L R |____| |______| TIP: To get the 3d depth, close one eye and focus on either left or right line, and then open it. This because the z axis uses x to get depth. Which means that you can get double depth to the image.... 4d depth??? :O p.s You're good teacher!
thank you, it helps me with my classwork. Blessings. : )
Why all of you guys placing vectors in matrix column by column you just do smth strange not RREF I mean you placed x x x y y y z z z Instead of x y z x y z x y z when you RREF second one you substract and adding some vectors to find depended once But actually thing that you did here seems to me wrong because you adding and substracting whole xs or whole ys or whole zs of different vectors WTF math always worked by logic,am i wrong or your solution is wrong,can someone explain
youre so good man!
Thank you
When you want to teach any concept, solve problem for generic values not for specific values.
👍
This video is by far the most thorough and best explanation. I love that Drew does a short review before solving the problem. He makes it so easy to understand the concept.
Thank you so much for the kind words!
cramming for an exam right now, ive watched tons of videos and read the entire textbook chapter, nothing helped me understand the topic better than this video. you are a godsend, i know this video is old but thank you so much!
So glad I could help! Hope your exam went well
best explanation of topic .... finally i understood the topic ... it is simple but our teacher make it very hard.
you made the most clear drawing of a linear algebra problem I have ever seen, it makes everything so much clearer to be able to understand which line, vector or plane is which, thank you
Bro left us and now we're stuck with mrs frost again- (Also the only other person in the comments ik is Michael- im suprised i havent seen anyone else ik) How many eggs could fit into a microwave 👨🦲
Your channel saved my butt for studying for a final.
asu?
@@kkshav_ wsu
There are two different topics I was trying to learn today and I was looking all over the internet for videos/clear explainations. Your channel is the only one with good videos in these topics. I really appreciate this. Thanks man I hope you make it big!
11:22 I think there is a mistake, it should be the span of {v1, v2, v3, v3} = span {v1, v2} , not span {v1, v2, v3 } = span v1, v2, since there are four vectors we started with in Col(A).
It was an example {v1, v2, v3, v3} = span {v1, v2} stands correct due to {v1, v2, v3 } = span {v1, v2} being correct
interesting you say that applying a linear transformation is 'shifting space'. So that is one way to think about it, as a mapping between two spaces , the departure space and the arrival space, or as transformation of the departure space. A linear transformation is equivalent to matrix multiplication, and for the null space we are looking for solutions to A*x = 0 , where x is an n x 1 matrix of "solutions" and A is a given m x n matrix. When x varies you have a map from R^n -> R^m , defined by x -> A * x .
drew im michael from f8f pls respond
my fav content creator drew werbowski
next upload when
Savior
You talk way too much, I just need the example
AWESOME EXPLANATION 🌟
thank you so much for making this video! :) I was wondering if you could possibly explain one-to-one and onto?
Thanks a lot, from India
what is there is a free variable in the reduced form?
For the Kernal you set the free variables of rref equal to t, s, r... , solve for each vector in terms of these, giving the span of the nul space aka kernal. For the Range you'd use the rref pivots/leading 1's , use only the corresponding columns from the original matrix, that should be your answer. Cool vid btw :)
Bro you're a goat I never comment but u made everything so much easier to understand than the other tutors who just yap about definitions, but you explain the intuition. Love it def gonna start watching u more for linear.
Thank you so much for your comment. Are there any linear algebra topics you would like to see?
@@DrewWerbowski Determine if U is or not a subspace with justification. Finding eigenvectors and eigenvalues and diagonalization. Gram-Schmidt Orthogonalization Algorithm and computing a projection Finding a basis for a vector space Finding the matrix that describes the linear transformation (9.1). Least Squares Approximation Singular Value Decomposition Proof of an important Theorem
@@Ahmed-yo7gb thank you for the comprehensive list! Many of those topics I already have videos on my channel, but I will add some of the others to my list
Good boy
Tysm
good job nerd, i actually learnt something
THANK YOU!!😀😀😀
Great video! Thanks
Thanks! You do just a great job of explaining this!
explained it better than my prof and my textbook combined. appreciate it man thank you