Linear algebra correct

A

AbdelRahmanShady

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Is this proof correct.
x + v = y + v
Then x = y in vector spaces
The proof:
x + v = x + v as addidtion is unique
by vecor space properties there is vector c where v + c = 0;
Add c to both sides
x + v + c = x + v + c is true as any vecor equals itself.
x + v + c = y + v + c
Then v + c = 0 so
x + 0 = y + 0
so x = y
Is this proof correct and rigorous
 
AbdelRahmanShady said:
Is this proof correct.
x + v = y + v
Then x = y in vector spaces
The proof:
x + v = x + v as addidtion is unique
by vecor space properties there is vector c where v + c = 0;
Add c to both sides
x + v + c = x + v + c is true as any vecor equals itself.
x + v + c = y + v + c → ................................... How does this statement come from line above ? you do not have 'y' inthe line above
Then v + c = 0 so
x + 0 = y + 0
so x = y
Is this proof correct and rigorous
Click to expand...
The proof:
x + v = x + v as addidtion is unique
by vecor space properties there is vector c where v + c = 0;
Add c to both sides
x + v + c = x + v + c is true as any vecor equals itself.
x + v + c = y + v + c → ................................... How does this statement come from line above ? you do not have 'y' inthe line above
Then v + c = 0 so
x + 0 = y + 0
so x = y
 
What did you do???!!!!
If V is a vector in a vector space, then so is -V. Use this fact to conclude that x=y
 
i have this statement by saying
x + v + c = x + v + c
(x + v) + c = (x + v) + c
hypothesis was x + v = y + v
so rhs = (y + v) + c
so is proof correct now
 
What is this c all about.
Here is the proof
To all: I decided to show this proof. Please respect my decision.

x + v = y + v
(x+v) + v' = (y+v) + v' (note that v' is the inverse of v)
Using the associate law we get x+(v+v') = y + (v+v')
Or x + (0) = y + (0)
x+0 = y+0
x=y using the property of the 0 vector
 
AbdelRahmanShady said:
i have this statement by saying
x + v + c = x + v + c
(x + v) + c = (x + v) + c
hypothesis was x + v = y + v
so rhs = (y + v) + c
so is proof correct now
Click to expand...
How can the proof be correct if you never concluded (correctly or incorrectly) that x=y??
 
Steven G said:
Steven G said:
How can the proof be correct if you never concluded (correctly or incorrectly) that x=y??
Click to expand...

What is this c all about.
Here is the proof
To all: I decided to show this proof. Please respect my decision.

x + v = y + v
(x+v) + v' = (y+v) + v' (note that v' is the inverse of v)
Using the associate law we get x+(v+v') = y + (v+v')
Or x + (0) = y + (0)
x+0 = y+0
x=y using the property of the 0 vector
Click to expand...
what i sent was why x + v + c = y + v + c
And c here is inverse of v and rest of proif is the first thing i said. I was asked why x + v + c = y + v + c thats why i added this bit to proof so our two proof will be the same. Last thing i am self learning this it is not a h.w or assignment or something so in general sharing there is no prpblem solutions
 
OK, I am sorry that I did not see that c=v'
You really need to show, as I did above, how you used the associate law.
 
AbdelRahmanShady said:
What do you mean
Click to expand...
Steven G said:
OK, I am sorry that I did not see that c=v'
You really need to show, as I did above, how you used the associate law.
Click to expand...
My prior post, which is below, clearly stated where I used the associative law of matrix addition.
x + v = y + v
(x+v) + v' = (y+v) + v' (note that v' is the inverse of v)
Using the associate law we get x+(v+v') = y + (v+v')
Or x + (0) = y + (0)
x+0 = y+0
x=y using the property of the 0 vector
 
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