Vector Spaces Mock Tests

Let V be the vector space of 2 × 2 matrices over ℝ. The dimension of the subspace of symmetric matrices in V is

The set S = {f ∈ C[0,1] : f(0) = 0} is a subspace of the vector space C[0,1].

The maximum number of linearly independent vectors in ℝ⁴ is

Let V be the vector space of all polynomials with real coefficients of degree at most 3. The dimension of V* (the dual space of V) is

Let V be the vector space of all 2 × 2 symmetric matrices over ℝ. The dimension of V is

The set of all polynomials with even degree (together with the zero polynomial) forms a subspace of the vector space of all polynomials over ℝ.