Linear Algebra Example Problems - Linear Combination of Vectors #2

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Given the vectors v1, v2, and v3, we see if the vector b can be written as a linear combination of the vectors.

This can be easily determined by constructing an augmented matrix, performing row operations, and finding the coefficients such that a1*v1 + a2*v2 + a3*v3 = b.

If values for a1, a2, and a3 can be found, then b is a linear combination of {v1,v2,v3} and we say that b is in the Span{v1,v2,v3}. If the augmented matrix has no solution, then b is NOT a linear combination of the vectors.

For this example, b CANNOT be written as a linear combination.

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This is the SHORTEST video that could give me the most HOLISTIC picture of linear combination and span!! Thank you!!

moushumipardesi

Fantastic explanation, short and straight to the point! 😀

RyanTW

These videos are helping me not only to pass but to get A’s in my linear algebra exams and assignments!!! Thank you ❤❤❤

valeriaacevedo

How to show that a vector of three components is a linear combination of two other three-components vectors?

ratanasorn

Thanks, thanks, thanks. It's very clear!

Thanks for making such videos, keep it up.

FidaHussain-mgzj

Sir is their any short trick for the purpose of competetive exams to get lc in 10-15 sec... Love u watch your videos.. Lots of love from India

healthygrownups

Adam Panagos if Alpha 2=0 and alpha 1, 3 are sum number after the reduce echelon form then what will be the solution linearly independent or dependent

abdullahghaffar

Before I proceed F grammarly.Now thank you for thjis vid

dexndi

would you please be my professor?
you are really good :)
thank you very much

firas

Good evening Adam, Don't get me wrong. I found your presentation clear, but what I do miss a bit is the geometric situation of the algebraic result, to show that vector b cannot be obtained from a linear combination of vectors X1, X2, and X3. Coincidentally I saw that X1=X3-X2, meaning that X1, X2, and X3 lie in the same plane within R3, so they are not linearly independent, and thus do not form a basis for R3. And apparently vector b does not lie in the plane spanned by (X1), X2, and X3. The conclusion is then that vector b cannot be a linear combination of (X1), X2, and X3. One final note, X1 can be considered redundant, hence the parentheses. I think this is the visualization of the algebraic result, or maybe not?! I'd like to understand what exactly happens given the result! (inconsistent system). Again Adam, this is not meant as a negative criticism of your video, but intended as a kind of supplement for a better understanding of the situation? I sometimes find Linear Algebra a bit confusing the way it is taught in general, and therefore not easy to study! best wishes and thanks, Jan-W

jan-willemreens