Question

The set of all n-tuples of real numbers of the form (x,x,x,......,x)with the standard operations on R^n. is this vector space or not

Answer 1

YES!

Answer 2

how

Answer 3

You need to trial all axiomus of vector space/. But it is so boring)

Answer 4

First you need to see if the the 0 vector is int he space, and it is, because (0,0,0,...,0,0) is in the form (x,x,x,x,.....,x,x)

Answer 5

give proof of some important axioms so that i get concept

Answer 6

let u=x and v=x then u+v=2x which is not equal to x axiom failed am i right

Answer 7

Then you need to check if its closed under addition, or in other words, if i add two vectors in that form, will the resulting vector still be in that form. So if i have a vector like (x,x,x,x,...,x,x), and (y,y,y,y,...,y,y), when i add them i get (x+y,x+y,....,x+y) . all the numbers in the vector are equal, so its good, its closed under addition

Answer 8

Then the last step is to check if its closed under scalar multiplication. if I have a vector (x,x,x,x,....x,x), and i multiply it by a scalar c, will the resulting vector still be in the form where every entry is the same? well, c times the vector gives (cx,cx,cx,cx,....,cx,cx), and every entry is the same, so it is closed under scalar multiplication.

Answer 9

And because this space has all three of these properties, is it a vector space. Is there anything you need me to clarify?

Answer 10

i got point thanks sir i have posted other problem can you see that