1. Determine if the given set W is a subspace of the given vector space V. If so, find a possible

basis for W and give the dimension of W.

{(²²

(b) V = M3x3(R), W = {A € M3x3(R) : AT

matrices with real coefficients

(a) V = M₂x2 (R), W

=

x² - y² x+y

I,VER}

-A}, the set of all skew-symmetric 3 x 3

x-Y xy

: y

=

(c) V = R₂(X), W = {(2a − 3b + 1) + (−2a + 5b)X + (2a + b)X²: a,b ≤ R}

(d) V = R4(X),

W = {ao + a₁X + a₂X² + a3X³ + a₁X : ao, a₁,..., an € R, ao + a₁ + a₂ + a3 + a₁ =0}