2.4 Given below are subsets of different vector spaces. Determine whether or not each subset is a subspace. You must prove your claim either way. a 2a] a. The subset of M32 consisting of all matrices of the form 3a 4a [5a 6al b. The set of all polynomials in P₂ of the form ax² + bx + c, where c≥ 0.

C. Let A be an m x n matrix. Then the orthogonal complement (Row (A)) of the row space of A is Nul(A), the null space of A. Select one: O True O False

II. Problem Solving/Proving. Show all complete solutions. 1. Show that V = M22, the set of all 2 x 2 matrix of real numbers, is a vector space with the usual addition of matrices and scalar multiplication. ( aj 2. Let VR2. Let V₁ = = [] and V₂ = be any two elements of R². Define and as follows: 02 V₁ V₂ = V₁ + V₂. and for any real number c cov = c(Av). 3 1 where A 22] Show that V is not a vector space. (F 5

Which of the following statements is false? Select one: O a. None of these. O b. The set of matrices of the form 1 c a,b ER is not a subspace of M2×2 O c. If A is a 2×3 matrix, then Nul A is a subspace of R3. O d. All planes in R3 are subspaces of R.