Do you have to notice that the rows are averages to do this problem? It seems like it is enough to realize that one of the vectors can be written as a linear combination of the other two because then you know that the space described by the column space of the matrix is at most two dimensional which is one less dimension than we need to describe a vector in R^3 like the one on the right hand side.
Just an FYI, the videos won't play for me at lem.ma in Chrome. I have autoplay turned off; maybe that's why. If I click on a video, I see the spinner but the video never starts. If I open an incognito window and log in, then the videos play.
Little light bulbs light for every video for me. Interesting I was thinking that [120,50,80] was unsolvable purely because there were linearly dependent columns which meant that span could not be the whole of R3 (not conclusive yet), and it was clearly not obtainable by any modifications to the original solution as the null space was the same (as you said). I guess this was sort of right but your observation was much clearer approach
The classes and the teacher’s teaching are excellent, fantastic! But I don't understand why some videos are without subtitles, not even in English. For non-native English speakers, understanding is very difficult. Could you fix this, @MathTheBeautiful?
I'm a bit confused about the definition of column space here. Isn't the column space the span of the decomposed vectors? If so, because column 2 is the average of 1 and 3, isn't the spans simply a plane in R3? And only by that definition, wouldn't the target vector fall inside the span?
Addressing your questions serial-wise 1) yes column space is defined as span of the column vectors we have in our matrix or the span of decomposed vectors 2)Yes , it spans simply a plane in R3 because there are only two independent vectors. 3) It may or may not be lie in the span of column vectors, it completely depends on the problem.
Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.
Do you have to notice that the rows are averages to do this problem? It seems like it is enough to realize that one of the vectors can be written as a linear combination of the other two because then you know that the space described by the column space of the matrix is at most two dimensional which is one less dimension than we need to describe a vector in R^3 like the one on the right hand side.
Hi professor. Would I be able to understand your tensor videos, if I watch all of your linear algebra videos?
You should watch all of my Linear Algebra videos regardless. (Preferably on lem.ma!) Tensors calculus requires multivariable calculus, too.
Just an FYI, the videos won't play for me at lem.ma in Chrome. I have autoplay turned off; maybe that's why. If I click on a video, I see the spinner but the video never starts. If I open an incognito window and log in, then the videos play.
Little light bulbs light for every video for me. Interesting I was thinking that [120,50,80] was unsolvable purely because there were linearly dependent columns which meant that span could not be the whole of R3 (not conclusive yet), and it was clearly not obtainable by any modifications to the original solution as the null space was the same (as you said). I guess this was sort of right but your observation was much clearer approach
Glad you're getting something out of my videos!
The classes and the teacher’s teaching are excellent, fantastic! But I don't understand why some videos are without subtitles, not even in English. For non-native English speakers, understanding is very difficult. Could you fix this, @MathTheBeautiful?
Please accept my apologies with regard to the lack of subtitles. I just don't have the bandwidth to do this.
I'm a bit confused about the definition of column space here. Isn't the column space the span of the decomposed vectors? If so, because column 2 is the average of 1 and 3, isn't the spans simply a plane in R3? And only by that definition, wouldn't the target vector fall inside the span?
Addressing your questions serial-wise
1) yes column space is defined as span of the column vectors we have in our matrix or the span of decomposed vectors
2)Yes , it spans simply a plane in R3 because there are only two independent vectors.
3) It may or may not be lie in the span of column vectors, it completely depends on the problem.
At 0:08 i didnt Understand what matrix you said