Which of the following sets are linear spaces? a) {X = (x1, x2, x3) in…

Which of the following sets are linear spaces?
a) {X = (x1, x2, x3) in R3 with the property x1 – 2×3 = 0}
b) The set of solutions x of Ax = 0, where A is an m × n matrix.
c) The set of 2 × 2 matrices A with det(A) = 0.
d) The set of polynomials p(x) with R1
-1 p(x) dx = 0.
e) The set of solutions y = y(t) of y” + 4y’ + y = 0.

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