Linearly Dependent Vectors | Example of Linearly Dependent Vectors

[@Violet-td5bt]

Thank you so much

[@roughshod174]

if you can take any value for c3, why cannot we take 0 as c3, it will result in another value having 0 besides c4??

[@eevibessite]

the trivial solution of the homogeneous system always exists. Here, the purpose is to look for non-zero scalar multiples (c1,c2,c3..... etc) in order to prove that one vector can be written as a multiple of another (to show the dependency).

[@Sahana-n8i]

If v substitute those values in c1v1+c2v2+c3v3+c4v4=0 v will get 0 as answer so it's linearly independent

[@eevibessite]

Only in case when any of these constants are non-zero

[@erukalaHimachandana]

But as per the condition if v1 is not equal to zero then it has to be independent??

[@eevibessite]

If you are asking about a single vector v1, then for sure

[@jasleenkaur645]

How can you say c3 is any real number?

[@eevibessite]

@@jasleenkaur645 because that's what we suppose while writing the linear combination equation. As we are looking for some constant multiple. This contant is chosen from the set of real (so that it can be positive or a negative number )

[@jasleenkaur645]

@@eevibessite smj nhi aya mam ese to hum koi bhi number lele khud se

[@eevibessite]

@jasleenkaur645 no, the number is chosen so that the equation is satisfied. So if I have 2 vectors v1=[3 3]and v2=[6 6] Then linear combination equation will be c1v1+c2v2=0 C1[3 3]+c2[6. 6]=0 As it can be observed easily that v2=2v1 Or if you rearrange , the equation becomes 2v1-v2=0 So here c1=2 and c2=-1

[@AsimKhan-kn5or]

thanks

[@asapvibes6323]

got me confused

[@eevibessite]

@@asapvibes6323 why ?

[@dineshpadhy7157]

Matalub c3 value aapne jarurat ke hisaba se le sakate he

[@eevibessite]

yes but any non-zero constant.

[@eevibessite]

Also watch here: kzbin.info/www/bejne/qneQiIaPeL-diaM

[@kirito1049]

Can explain the part where v1 bevame linear dependent

[@kirito1049]

Like where finding whether v1 is linear independent

[@webcraft3315]

thank alot

[@dukeontiri2363]

nice one

[@eevibessite]

Thanks

[@sagarpandey2762]

How will we choose upper triangular matrix ?

[@eevibessite]

What do you mean by choosing ? We convert the matrix into upper triangular matrix by performing elementary row operations

[@olatunjiOlayinka970]

How did you know c3 was 1

[@yashasvithakur9078]

c3 belong to real number so we can take any value acc to our own convenience