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=Basis Problems= | =Basis Problems= | ||
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| + | Example #1: Polynomials | ||
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| + | :Part 1:Is the set of polynomials <math> x^2, x, and 1 </math> a basis for the set of all polynomials of degree two or less? | ||
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| + | :::quick solution | ||
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| + | :::rigorous solution | ||
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| + | :Part 2: is the set of polynomials <math> 3x^2, x and 1 </math> a basis for the set of all polynomials of degree two or less? | ||
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| + | :::quick solution: | ||
| + | |||
| + | :::rigorous solution: | ||
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| + | :Part 3: is the set of polynomials <math> 3x^2 + x, x and 1 </math> a basis for the set of all polynomials of degree two or less? | ||
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| + | :::quick solution: | ||
| + | |||
| + | :::rigorous solution: | ||
| + | |||
| + | :Part 4: is the set of polynomials <math> 3x^2+x+1, 2x+1, and 2 </math> a basis for the set of all polynomials of degree two or less? | ||
| + | :::quick solution: | ||
| + | :::rigorous solution: | ||
| + | |||
| + | :Part 5: is the set of polynomials <math> x^3, x, and 1 </math> a basis for the set of all polynomials of degree two or less? | ||
| + | :::quick solution: | ||
| + | :::rigorous solution: | ||
| + | |||
| + | :Part 6: is the set of polynomials <math> x^2,3x^2, x and 1 </math> a basis for the set of all polynomials of degree two or less? | ||
| + | :::quick solution: | ||
| + | :::rigorous solution: | ||
| + | |||
| + | :Part 7: is the set of polynomials <math> x^2,3x^2 + 1, x and 1 </math> a basis for the set of all polynomials of degree two or less? | ||
| + | :::quick solution: | ||
| + | :::rigorous solution: | ||
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| + | |||
| + | :Part 8: is the set of polynomials <math> x^2, x and 1 </math> a basis for the set of ALL POLYNOMIALS? | ||
| + | :::quick solution: | ||
| + | :::rigorous solution: | ||
| + | |||
| + | :Part 9: | ||
Revision as of 09:03, 12 March 2013
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:
