Concept explainers
The polynomials of degree less than 7 form a seven dimensional subspace of the linear space of all polynomials.
To verify the statement “The polynomials of degree less than 7 form a seven-dimensional subspace of the linear space of all polynomials” is true or false.
Answer to Problem 1E
Given statement is true.
Explanation of Solution
Given: The polynomials of degree less than 7 form a seven-dimensional subspace of the linear space of all polynomials
The polynomials of degree less than 7 contains neutral element 0 of the linear space of all polynomials, it is closed under addition and scalar multiplication.
The dimension of the polynomials of degree less than 7 is at most 7.
Hence given statement is true.
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