Question

Recall $P_3 = {ax^3 + bx^2 + cx + d mid a, b, c, d in mathbb{R}}$ is the set of polynomials of degree at most 3. Consider the subspace $A = {p in P_3 : p(5) = p(3) = 0}$. Select ALL sets that form a basis for A. ${(x - 5)(x - 3)x}$ ${x - 5, x - 3}$ ${2(x - 5)(x - 3), (x - 5)(x - 3)x}$ ${(x - 5)(x - 3), (x - 5)(x - 3)x}$ ${x, x - 5, x - 3}$ ${(x - 5)(x - 3)}$

          Recall $P_3 = {ax^3 + bx^2 + cx + d mid a, b, c, d in mathbb{R}}$ is the set of
polynomials of degree at most 3.
Consider the subspace $A = {p in P_3 : p(5) = p(3) = 0}$.
Select ALL sets that form a basis for A.
${(x - 5)(x - 3)x}$
${x - 5, x - 3}$
${2(x - 5)(x - 3), (x - 5)(x - 3)x}$
${(x - 5)(x - 3), (x - 5)(x - 3)x}$
${x, x - 5, x - 3}$
${(x - 5)(x - 3)}$

Recall P3 = ax^3 + bx^2 + cx + d mid a, b, c, d in mathbbR is the set of
polynomials of degree at most 3.
Consider the subspace A = p in P3 : p(5) = p(3) = 0.
Select ALL sets that form a basis for A.
(x - 5)(x - 3)x
x - 5, x - 3
2(x - 5)(x - 3), (x - 5)(x - 3)x
(x - 5)(x - 3), (x - 5)(x - 3)x
x, x - 5, x - 3
(x - 5)(x - 3)

Added by Jamie M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ishana K

03/31/2022

Step 1

** Show more…

Show all steps

Thanks for your feedback!

Recall P3 = {ax^3 + bx^2 + cx + d | a, b, c, d in R} is the set of polynomials of degree at most 3. Consider the subspace A = {p in P3 : p(5) = p(3) = 0}. Select ALL sets that form a basis for A. {(x - 5)(x - 3)x} {x - 5, x - 3} {2(x - 5)(x - 3), (x - 5)(x - 3)x} {(x - 5)(x - 3), (x - 5)(x - 3)x} {x, x - 5, x - 3} {(x - 5)(x - 3)}