- #1
Baartzy89
- 16
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Hi all,
I'm preparing for a deferred exam this semester after falling ill last year. Just looking over my course notes and have a question. I understand how this works in the big picture scheme. What I don't understand however is how my instructor simplified the original equation.
1. Homework Statement
Step 1) (1-t)z1 + t*(z2+z3/2) = (1-s)z1 + s(z2+z3/2)
Step 2) Simplifies to;
(2-s)z1+(t-2+2s)z2+(t-s)z3 = 0
Since z1, z2 and z3 aren't collinear, their coefficients in this equation must be zero. Therefore we have;
a) 2-s-2t = 0
b) t-2+2s = 0
c) t-s = 0
Then we readily find t = s = 2/3
Which is then substituted into the original equation for medians to find that it equals (z1+z2+z3)/3
I understand how this works in the big picture scheme. What I don't understand however is how my instructor simplified the original equation step 1 to step 2.[/B]
My attempt from equating the equations;
(1-t)z1 + t*(z2+z3/2) = (1-s)z1 + s(z2+z3/2)
0 = (2-s)z1+(t-2+2s)z2+(t-s)z3
= (1-s)z1 + s(z1+z3/2) + s(z2+z3/2) - (1-t)z1 - s(z2+z3/2)
= z1 - s*z1 - z1 + t*z1 - s*(z2/2) - s*(z3/2) + s*(z2/2) + s*(z3/2)
= t*z1 - s*z1
Therefore t*z1 = s*z1 and divide both sides by z1 t = s
I feel this comes out slightly like my instructors, but its faulty somewhere...
I'm preparing for a deferred exam this semester after falling ill last year. Just looking over my course notes and have a question. I understand how this works in the big picture scheme. What I don't understand however is how my instructor simplified the original equation.
1. Homework Statement
Step 1) (1-t)z1 + t*(z2+z3/2) = (1-s)z1 + s(z2+z3/2)
Step 2) Simplifies to;
(2-s)z1+(t-2+2s)z2+(t-s)z3 = 0
Since z1, z2 and z3 aren't collinear, their coefficients in this equation must be zero. Therefore we have;
a) 2-s-2t = 0
b) t-2+2s = 0
c) t-s = 0
Then we readily find t = s = 2/3
Which is then substituted into the original equation for medians to find that it equals (z1+z2+z3)/3
Homework Equations
I understand how this works in the big picture scheme. What I don't understand however is how my instructor simplified the original equation step 1 to step 2.[/B]
The Attempt at a Solution
My attempt from equating the equations;
(1-t)z1 + t*(z2+z3/2) = (1-s)z1 + s(z2+z3/2)
0 = (2-s)z1+(t-2+2s)z2+(t-s)z3
= (1-s)z1 + s(z1+z3/2) + s(z2+z3/2) - (1-t)z1 - s(z2+z3/2)
= z1 - s*z1 - z1 + t*z1 - s*(z2/2) - s*(z3/2) + s*(z2/2) + s*(z3/2)
= t*z1 - s*z1
Therefore t*z1 = s*z1 and divide both sides by z1 t = s
I feel this comes out slightly like my instructors, but its faulty somewhere...