The set is a vector space The set of 2 by 2 matrices with in

The set is a vector space. The set of 2 by 2 matrices with integer entries. R^3. The empty set. The interior of the circle of radius 1 centered at the origin in the xy plane. P_4(R) The set of real valued continuous function defined on the interval [0, 1]. The set of points (x, y, z) in R^3 that satisfy x^2 + 3y^2 + 12z^2 = 0. The set of points (x, y, z) in R^3 that satisfy -3x + 2y + 11z = 0. The set of polynomials p in P_3 (R) that satisfy integral_0^1 p(x) dx = 0. The set of polynomials p in P_2(R) that have no real or complex roots.

Solution

true is given below

these set are vector space

1

2

3

6

7

8

other set are not vector space

that are false