Find a basis and calculate the dimension of the following subspaces of R4. (a) U-{[a a +

Question:

Find a basis and calculate the dimension of the following subspaces of R4.
(a) U-{[a a + b a-b b]T|a and b in R}.
(b) U={[a + b a-b b a]T | a and b in R}.
(c) U={[a b c + a c]T |a, b, and c in R}.
(d) U= {[a - b b + c a b + c]T | a, b, and c in R}.
(e) U={[a b c d]T | a + b - c + d = 0 in R}.
(f) U={[a b c d]T |a + b = c + d in R).