#Affine combination problem

33 messages · Page 1 of 1 (latest)

toxic lichen
#

I solved the question but i dont think im applying the necessary condition to check for affine combination .

image.png
tacit havenBOT
#
  1. Wait patiently for a helper to come along.
  2. Once someone helps you, say thank you and close the thread with:
+close
  1. Feel free to nominate the person for helper of the week in #helper-nominations
  2. Do not ping the mods, unless someone is breaking the rules.
  3. If you're happy with the help you got here, and the server overall, you can contribute financially as well:
toxic lichen
#

i just solved this equation for c1v2 + c2v2 + c3v3 = y

#

and in the end i am getting y = y after finding my constants

#

but im not getting c1 + c2 + c3 = 1

#

so its not fulfilling the condition for affine combination

ashen galleon
toxic lichen
#

im not getting c1 + c2 +c3 = 1

#

but im getting y = y

#

so that means y cannot be written as an affine combination of v1 v2 v3?

ashen galleon
#

$$ \begin{cases} c_1v_1+c_2v_2+c_3v_3 = y \ c_1+c_2+c_3 = 1 \end{cases} $$

leaden pawnBOT
ashen galleon
#

this is the system you solve

toxic lichen
#

so i solve both of these together? or i solve c1v1+c2v2+c3v3 = y this first to get the values of my constants

ashen galleon
#

no you don't solve one of them first, they are a part of the same system

#

you have to solve the system

toxic lichen
#

can you please explaint a bit on how to solve this system?

ashen galleon
#

$$ \begin{cases}-3c_1 + 0c_2 + 4c_3 = 17 \ c_1 + 4c_2 -2c_3 = 1 \ c_1 -2c_2 + 6c_3 = 5 \ c_1+c_2+c_3 = 1 \end{cases} $$

leaden pawnBOT
ashen galleon
#

3 parameters, 4 conditions

toxic lichen
#

oh ok

#

wait i have one more question

#

its related to this

#

c1v1 + c2v2 +c3v3 +c4v4 = 0
c1 + c2 + c3 + c4 = 0

#

this is the system i will solve in this one?

ashen galleon
#

yes and the solution must be nonzero

#

by definition

toxic lichen
#

ok

#

thanks

#

+close