Which of the following subsets are subspaces of the space of 2 × 2 matrices under the usual matrix operations.

1.The set of matrices of the form

[a −a]

[b 0]

where a and b are arbitrary real numbers.

2.The set of symmetric 2 × 2 matrices.

3.The set of singular 2 × 2 matrices.

Which of the following subsets are subspaces of the space of polynomilas of degree at most 5.

1. The set of polynomials for which the sum of all coefficients is equal to zero.

2. The set of polynomials f(x) such that f(2) = f(3).

3. The set of polynomials f(x) such that f'(2) = 1.