Do the vectors x3 1 x2 x x 2 span P3 Recall that P3 is th

Do the vectors x^3 + 1, x^2 + x, x + 2 span P_3? (Recall that P_3 is the set of all polynomials of degree at most 3).

Standard basis for P3 is:

{1,x,x^2,x^3}

which is set of 4 linearly independent vectors. So P3 has dimension 4 and needs a minimum of 4 vectors to span

So given set of 3 vectors does not span P3

$Do the vectors x^3 + 1, x^2 + x, x + 2 span P_3? (Recall that P_3 is the set of all polynomials of degree at most 3).SolutionStandard basis for P3 is: {1,x,x^2$

Do the vectors x3 1 x2 x x 2 span P3 Recall that P3 is th

Solution

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