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

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ParthKohliBest ResponseYou've already chosen the best response.0
I am overrated. I don't know all this stuff!
 one year ago

hbaBest ResponseYou've already chosen the best response.1
I also do not know this stuff,I am just starting.
 one year ago

hbaBest ResponseYou've already chosen the best response.1
I know we can use wronskian,determinant and definition. Can you explain me by definition ?
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
well 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 :)
 one year ago

hbaBest ResponseYou've already chosen the best response.1
Please explain further and in depth :)
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
lets 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
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
if 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
 one year ago

hbaBest ResponseYou've already chosen the best response.1
Thanks a lot for helping,I got it :)
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
you'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
 one year ago

hbaBest ResponseYou've already chosen the best response.1
@ghazi What :o Won't that be linearly independent ?
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
if \[V _{1}= K V_{2}\] 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
 one year ago

hbaBest ResponseYou've already chosen the best response.1
I am so confused Just answer me Linearly dependent or linearly indepdent ?
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
look 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
 one year ago

hbaBest ResponseYou've already chosen the best response.1
Thanks a lot dude got it :)
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
if 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
 one year ago

hbaBest ResponseYou've already chosen the best response.1
What if there are only two vectors ?
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
then 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
 one year ago

hbaBest ResponseYou've already chosen the best response.1
So for my question would it be like, dw:1358511169334:dw
 one year ago

hbaBest ResponseYou've already chosen the best response.1
@ghazi I know that but i am trying to learn all the methods.
 one year ago

hbaBest ResponseYou've already chosen the best response.1
@ghazi Did i do this correctly ?
 one year ago

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