What properties of vector space fail to hold the following:
The set of all ordered triples of real numbers with the operations:
U = (a,b,c), V = (x,y,z), r is a real number.
Vector Addition: U + V = (a+x, b+y, c+z)
Scalar Multiplication: r * U = (a, 1, c)
I am fine with addition properties. They hold true. I am confused with scalar multiplication.
Appreciate your help.