Question

Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set of all seventh-degree polynomials with the standard operations

Answer 1

Answer:

Following are the solution to this question:

Step-by-step explanation:

Let X is a set of all polynomials of the third-degree with regular operations.  

This set is not a space for a vector since it is not shut down  

For instance:

$\to x^3+3x^2+2 \in X \ \ \ and \ \ \ -x^3+2x^2+2x \in X$

Calculating the sum:

$\to x^3+3x^2+2 + -x^3+2x^2+2x\\\\\to 5x^2+2x+2 \notin X$

That's why X isn't a space for vectors because X isn't shut down.