Linear Algebra Example Problems - Linear Combination of Vectors #1

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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 CAN be written as a linear combination.
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[@TheOnlyRealBreadIntheWorld]

Thank you so much. You are a lifesaver. The world always needs great teachers like you

[@AdamPanagos]

Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam

[@eldiospadre128]

Short, to the point, well-explained. Excellent video!

[@AdamPanagos]

+Diego Rivera Thanks, glad you liked it!

[@ED-ix6mq]

Awesome explanation, thank you very much!

[@janakicharles2701]

This is such a brilliant way of explaining this topic.

Thanks. Your explanation is very clear.

[@keithgotami6415]

excellent video...very helpful

[@petitbonheur4524]

But is b still a linear combination of these vectors if let's say one of the columns is a free variable column, we just have to write our alphas in parametric form right???

[@sanjoytanwi]

Thanks for nice and well explanation.

[@AdamPanagos]

+Sanjoy Tanwi Glad you liked it, thanks for the nice comment.

[@sheikhhashir836]

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[@AdamPanagos]

Glad I could help, thanks for watching. If you’re looking for additional examples/videos make sure to check out my website adampanagos.org where I have a lot of other videos and resources available that you might find helpful. Thanks, Adam.

[@mannanmana1538]

Very nice video

[@skyisblueyeaitis6262]

thank you sir
its really helpful

[@AdamPanagos]

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content you might find helpful. Thanks, Adam

[@meenamena5758]

Express the vector (3,5,2) as a linear combination of the vectors (1,1,0,) (2,3,0) and (0,0,1) of v3 (R) pz solved madi kodi

[@user-bu8mg7uq3s]

thanks

[@marcushines4172]

Thank you

[@AdamPanagos]

+Marcus Hines You're welcome, thanks for watching!

[@fahimnazari62]

well explained
1:03

[@kinza7549]

+Fahim Nazari lmao

[@higgo7475]

awesome vid

[@AdamPanagos]

Glad you liked it; thanks for watching.

[@kesarikr6679]

well explained

[@AdamPanagos]

Glad I could help, thanks for watching. If you’re looking for additional examples/videos make sure to check out my website adampanagos.org where I have a lot of other videos and resources available that you might find helpful. Thanks, Adam.

[@AtifKhan-kk2nm]

Thanks ☺️

[@AdamPanagos]

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

[@xolanimavuso6989]

1:03

[@mbusomabuza7273]

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[@Herotruth]

Why didn't you show one that was not so we can see the difference?

[@Herotruth]

nevermind I saw the second video, lol

[@EmapMe]

Did you really have to solve this using a matrix? Wouldnt it be way easier to just solve it normally?

[@nina755]

wtf is raw operation

[@buthainaalmaskari9662]

Gauss Jordan Elimination to make it reduced echelon form

[@ChiddyChiddy01]

*row operation