Recall that a plane in R3 can be described by the equation n

Recall that a plane in R3 can be described by the equation n. (x y z) = n . P where the vector p labels a given point on the plane and n is a vector normal to the plane. Let N and P be vectors in R101 and X = (x1 x2 : x101) What kind of geometric object does N. X = N . P describe?

Solution

N and P vectors are in the R^(101) space basically they are the vectors of the size (101) X (101)

By multiplying the vector with 101 X 1 (being the x vector)

N.X = N. P = (101 X 101) X (101 X 1) = (101 X 1)

Hence the resultant vector will solve the 101 variable equations, with the parameters x1,x2,...,x101 and equating it to the value