17:55, watching at 69 views ^^ Btw, do you have a patreon or something like that? Because your videos are really helping me with learning the math for a machine learning book I'm currently reading and I'd be happy to support you in some way :] (I've been looking a long time for structured, complete and well explained courses about linear algebra and calculus and am happy I finally found them!)
What is the difference between the span of d and U in example 8?Is the span of d not equal to U? Don't they both share the same line through the origin? If this is the case, why did you have to say the span of d belongs to U if we already know U has the same span as the span of d. I am confused because @41:28 , you state that the span of vector d belongs to U.
The second example is incorrect, if you do the k3 for both of the equations it needs to work for there is not a single number that can be found, also if you check what is said at the end of the problem, the vectors don't add up.
I'm sure there is a small typo somewhere but the method is still fine. I'll correct the typo and reupload the video when I have time so thank you for pointing it out.
Oh ya so because we got 0=0, that implies anything that solves one of the equation will solve the other one. So, let us take 4=2(c1)-3(c2) Using some algebra, (c1) = 2+(3/2)*(c2) which gives us a function that can determine the constants for linear combinations.
17:55, watching at 69 views ^^
Btw, do you have a patreon or something like that? Because your videos are really helping me with learning the math for a machine learning book I'm currently reading and I'd be happy to support you in some way :] (I've been looking a long time for structured, complete and well explained courses about linear algebra and calculus and am happy I finally found them!)
I'm setting up one when I get around to doing it :) .
What is the difference between the span of d and U in example 8?Is the span of d not equal to U? Don't they both share the same line through the origin? If this is the case, why did you have to say the span of d belongs to U if we already know U has the same span as the span of d.
I am confused because @41:28 , you state that the span of vector d belongs to U.
The second example is incorrect, if you do the k3 for both of the equations it needs to work for there is not a single number that can be found, also if you check what is said at the end of the problem, the vectors don't add up.
I'm sure there is a small typo somewhere but the method is still fine. I'll correct the typo and reupload the video when I have time so thank you for pointing it out.
Example 3 has solutions though right? All points lie on y=5x and the span of v1 and v2 is y=5x
Oh ya so because we got 0=0, that implies anything that solves one of the equation will solve the other one.
So, let us take 4=2(c1)-3(c2)
Using some algebra, (c1) = 2+(3/2)*(c2) which gives us a function that can determine the constants for linear combinations.
@@jkgan4952 Yeah I get it. I guess I was meaning to say that there is no unique solution to this system.