Consider the following vector spaces V and subsets U. Determine if U is a subspace of V. Make sure to justify your findings.
a) V = R3
U = All vectors of the form (a, b, c), where b=a+c+1.
b) V = Set of all 3 x 3 matrices.
U = Set of 3 x 3 upper triangular matrices.
(You may consider regular matrix addition and scalar multiplication.)
c) V = P(2), set of all quadratic polynomials (ax² + bx + c)
U = Set of quadratic polynomials whose coefficients add up to 1.
For example, 3x²+2x-4, x²-x+1,423)