In Exercises 11 – 15 which of the sets S are subspaces? 11. S = {(a,b, c) E R³ : a > 0, b > 0, c> 0}. {(x1, x2, x3) E R° 0 where a1, a2, a3 E R are fixed}. 12. S = a1x1 + a2x2 + a3x3 : R² {(x, y) (x,...

Please help. This problem involves vector subspaces. One picture includes sets 11-13 and the other includes sets 14-15.

Extracted text: In Exercises 11 – 15 which of the sets S are subspaces? 11. S = {(a,b, c) E R³ : a > 0, b > 0, c> 0}. {(x1, x2, x3) E R° 0 where a1, a2, a3 E R are fixed}. 12. S = a1x1 + a2x2 + a3x3 : R² {(x, y) (x, y) is on the line through (1, 1) with slope 1}. 13. S :


Extracted text: 14. S= {x E R' : Ax = 0} where A is a 3 × 2 matrix. 15. S {x € R : Ax = b} where A is a 3 x 2 matrix and 3 bE R° is a fixed nonzero vector.