1. Let U = {r, s, t,
u, v, w, x, y,
z}, D = {s, t, u,
v, w}, E = {v, w,
x}, and F = {t, u}. Use roster
notation to list the elements of D ∩ E.
a.
{v, w}
b.
{r, s, t, u, v,
w, x, y, z}
c.
{s, t, u}
d.
{s, t, u, v, w,
x, y, z}
2. Let U = {r, s,
t, u, v, w, x,
y, z},...
1. Let V and W be vector spaces over R.
a) Show that if T: V → W and S : V → W are both linear
transformations, then the map S + T : V → W given by (S + T)(v) =
S(v) + T(v) is also a linear transformation.
b) Show that if R: V → W is a linear transformation and λ ∈ R,
then the map λR: V → W is given by (λR)(v) =...