Basis Problems
Example #1: Polynomials
- Part 1:Is the set of polynomials $ x^2, x, and 1 $ a basis for the set of all polynomials of degree two or less?
- quick solution
- rigorous solution
- Part 2: is the set of polynomials $ 3x^2, x and 1 $ a basis for the set of all polynomials of degree two or less?
- quick solution:
- rigorous solution:
- Part 3: is the set of polynomials $ 3x^2 + x, x and 1 $ a basis for the set of all polynomials of degree two or less?
- quick solution:
- rigorous solution:
- Part 4: is the set of polynomials $ 3x^2+x+1, 2x+1, and 2 $ a basis for the set of all polynomials of degree two or less?
- quick solution:
- rigorous solution:
- Part 5: is the set of polynomials $ x^3, x, and 1 $ a basis for the set of all polynomials of degree two or less?
- quick solution:
- rigorous solution:
- Part 6: is the set of polynomials $ x^2,3x^2, x and 1 $ a basis for the set of all polynomials of degree two or less?
- quick solution:
- rigorous solution:
- Part 7: is the set of polynomials $ x^2,3x^2 + 1, x and 1 $ a basis for the set of all polynomials of degree two or less?
- quick solution:
- rigorous solution:
- Part 8: is the set of polynomials $ x^2, x and 1 $ a basis for the set of ALL POLYNOMIALS?
- quick solution:
- rigorous solution:
- Part 9:
