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hba
 4 years ago
Show that the following vectors are linearly independent.(Over C or R)
(1,1,1) and (0,1,2)
hba
 4 years ago
Show that the following vectors are linearly independent.(Over C or R) (1,1,1) and (0,1,2)

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ParthKohli
 4 years ago
Best ResponseYou've already chosen the best response.0I am overrated. I don't know all this stuff!

hba
 4 years ago
Best ResponseYou've already chosen the best response.1I also do not know this stuff,I am just starting.

hba
 4 years ago
Best ResponseYou've already chosen the best response.1I know we can use wronskian,determinant and definition. Can you explain me by definition ?

Ghazi
 4 years ago
Best ResponseYou've already chosen the best response.4well for these two vectors to be linearly DEPENDENT, vector 1 should be able to be expressed as product of a constant and the another vector which means \[V _{1}=KV _{2}\] is this helpful ? or shall i explain further :)

hba
 4 years ago
Best ResponseYou've already chosen the best response.1Please explain further and in depth :)

Ghazi
 4 years ago
Best ResponseYou've already chosen the best response.4lets say \[V _{1}= i+ j+k \] and vector \[V _{2}=j2k\] now we can see that \[V _{1} \neq KV _{2}\] therefore these are linearly independent vectors

Ghazi
 4 years ago
Best ResponseYou've already chosen the best response.4if we had two vectors like \[V _{1}= i+j+k\] and \[V _{2}= 2i +2j+ 2k\] we can easily see that \[V _{1}=k V _{2}\] therefore these two are linearly dependent vectors , wherever this condition fails , it means vectors are independent

hba
 4 years ago
Best ResponseYou've already chosen the best response.1Thanks a lot for helping,I got it :)

Ghazi
 4 years ago
Best ResponseYou've already chosen the best response.4you're welcome but do look for three vectors too , it uses determinant technique , in the above example we can see that V1=2 V2 , so its dependent

hba
 4 years ago
Best ResponseYou've already chosen the best response.1@ghazi What :o Won't that be linearly independent ?

Ghazi
 4 years ago
Best ResponseYou've already chosen the best response.4if \[V _{1}= K V_{2}\] then its dependent because you can see that one can be expressed in terms of other but if this condition fails then both the vectors are independent

hba
 4 years ago
Best ResponseYou've already chosen the best response.1I am so confused Just answer me Linearly dependent or linearly indepdent ?

Ghazi
 4 years ago
Best ResponseYou've already chosen the best response.4look if \[V _{1}= K V_{2}\] now , if \[V _{1}=i+j+k\] and \[V _{2}= 2i+2j+2k\] then we can see that \[V _{1}=2 *V _{2}\] therefore these vectors are LINEARLY DEPENDENT BUT IF THIS CONDITION FAILS AND ONE VECTOR IS NOT EXPRESSED BY THE HELP OF CONSTANT TO THE ANOTHER ONE THEN ITS INDEPENDENT WHICH MEANS \[V _{1} \ne K V _{2}\] as the two vectors given in your question :D

hba
 4 years ago
Best ResponseYou've already chosen the best response.1Thanks a lot dude got it :)

Ghazi
 4 years ago
Best ResponseYou've already chosen the best response.4if you have three vectors like \[V _{1}=i+2j+3k\]\[V _{2}= 2i+j+3k\]\[V _{3}= i+j+k\] then you have to take determinant of these p elements that is the coefficients of i, j, k in all the three vectors dw:1358510982059:dw if the determinant is zero then vectors are linearly independent

hba
 4 years ago
Best ResponseYou've already chosen the best response.1What if there are only two vectors ?

Ghazi
 4 years ago
Best ResponseYou've already chosen the best response.4then form a determinant of 2 x 2 and check if its mod is zero or not but the method that i told you earlier is easier for two vectors

hba
 4 years ago
Best ResponseYou've already chosen the best response.1So for my question would it be like, dw:1358511169334:dw

hba
 4 years ago
Best ResponseYou've already chosen the best response.1@ghazi I know that but i am trying to learn all the methods.

hba
 4 years ago
Best ResponseYou've already chosen the best response.1@ghazi Did i do this correctly ?

Ghazi
 4 years ago
Best ResponseYou've already chosen the best response.4do you think you can take determinant of the 2 x 3 elements that you have formed , i dont think so
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