I have been looking for an explanation for this question and I finally found your video, so I could solve my question after hours of searching. Thanks for the explanation. You´re one and only. You´re the best. Thank you again!!!
Thanks for the explanation ! Really helpful to first write what it even means for a vector to be in a sum or an intersection. I kept accidentally doing the basis of a sum for an intersection instead of understanding correctly what it means
If you translate the final matrix at 3:33 to a linear system on 4 variables a_1,a_2,a_3,a_4, it reads: a_1+a_4=0 a_2+a_4=0 a_3+a_4=0 0=0 The last question is true but meaningless. Since the matrix is fully reduced, all other equations are independent of each other, and, given that they're 3 such equations and you have 4 variables, one of the variables is independent, while the other 3 are dependent. In this case we are able to choose that a_4 is the "free variable", and the other variables depend on a_4. Thus, given any value of a_4, the others are determined as a_1=-a_4, a_2=-a_4, a_3=-a_4. If you choose the value of a_4 as "s" (s is any real number), you get the answer in the video.
I have been looking for an explanation for this question and I finally found your video, so I could solve my question after hours of searching. Thanks for the explanation. You´re one and only. You´re the best. Thank you again!!!
Thank u, your videos are a gift from god
Thanks for the explanation ! Really helpful to first write what it even means for a vector to be in a sum or an intersection. I kept accidentally doing the basis of a sum for an intersection instead of understanding correctly what it means
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Gnuoil😅😅😅😊❤😮😢😮🎉
QUEEN
true
Thank you! Helped me a lot
i dont understand where did you get the values of s from?
still wondering
If you translate the final matrix at 3:33 to a linear system on 4 variables a_1,a_2,a_3,a_4, it reads:
a_1+a_4=0
a_2+a_4=0
a_3+a_4=0
0=0
The last question is true but meaningless. Since the matrix is fully reduced, all other equations are independent of each other, and, given that they're 3 such equations and you have 4 variables, one of the variables is independent, while the other 3 are dependent. In this case we are able to choose that a_4 is the "free variable", and the other variables depend on a_4. Thus, given any value of a_4, the others are determined as a_1=-a_4, a_2=-a_4, a_3=-a_4. If you choose the value of a_4 as "s" (s is any real number), you get the answer in the video.
3:44 , i did not understand where this s came from.
my hero
So is basis u1 u2 v1 v2?
wonderfully explained ma'am
How a1=-s is it not equal to s?
a + s = 0 so a = -s and not s
Thanks
Why a1 is equal to -S?
@@AnimeReaction4K Don't know how much it helped the original commenter, but it sure helped me. So thank you, kind stranger
3:09