hba
  • hba
Show that the following vectors are linearly independent.(Over C or R) (1,1,1) and (0,1,-2)
Linear Algebra
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
hba
  • hba
@Hero
ParthKohli
  • ParthKohli
I am overrated. I don't know all this stuff!
hba
  • hba
No worries c:

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

hba
  • hba
@phi
hba
  • hba
I also do not know this stuff,I am just starting.
hba
  • hba
I know we can use wronskian,determinant and definition. Can you explain me by definition ?
hba
  • hba
@zaynahf
ghazi
  • ghazi
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 :)
hba
  • hba
Please explain further and in depth :)
ghazi
  • ghazi
lets say \[V _{1}= i+ j+k \] and vector \[V _{2}=j-2k\] now we can see that \[V _{1} \neq KV _{2}\] therefore these are linearly independent vectors
ghazi
  • ghazi
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
hba
  • hba
Thanks a lot for helping,I got it :)
ghazi
  • ghazi
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
hba
  • hba
@ghazi What :o Won't that be linearly independent ?
ghazi
  • ghazi
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
hba
  • hba
I am so confused Just answer me Linearly dependent or linearly indepdent ?
ghazi
  • ghazi
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
hba
  • hba
Thanks a lot dude got it :)
ghazi
  • ghazi
you're welcome :D
ghazi
  • ghazi
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
hba
  • hba
What if there are only two vectors ?
ghazi
  • ghazi
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
hba
  • hba
So for my question would it be like, |dw:1358511169334:dw|
hba
  • hba
@ghazi I know that but i am trying to learn all the methods.
hba
  • hba
@ghazi Did i do this correctly ?
ghazi
  • ghazi
do you think you can take determinant of the 2 x 3 elements that you have formed , i dont think so

Looking for something else?

Not the answer you are looking for? Search for more explanations.