prove if u is a vector in Rn and a and b are scalars then ab

prove: if u is a vector in R^n and a and b are scalars, then (a+b)u= au+but.

Solution

We can prove this by distributive property of scalar multiplication. This theorem states that if c and d are two scalars and v be a vector in R^n then (c+d)v= cv+dv.

Using the above property we can say that

(a+b)u= au+bu