Solve only 3.1.4. Exercise In the first ten exercises determine whether the given set describes a vectorspace or not. For each function space the operations are defined by Equa-tions 3.1 and 3.2. Explain your answers!Exercise 3.1.1. The set of all polynomials of degree two and the zero poly-nomial.Exercise 3.1.2. The set of all solutions (x, y) of the equation 2x + 3y = 0,with addition and multiplication by scalars defined as in R².Exercise 3.1.3. The set of all solutions (x, y) of the equation 2x + 3y = 1,with addition and multiplication by scalars defined as in R².Exercise 3.1.4. The set of all twice differentiable functions f for whichf"(x) +2f(x) = 0 holds.

Ans-3.14 The differential equation f''(x) + 2f(x) = 0---------------(1) is a second-order linear…

Answered: Exercise 3.1.4. The set of all twice…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 30E

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Similar questions

Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1) is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.
Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Find a basis for R2 that includes the vector (2,2).
Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are linearly dependent in the vector space C[0,1], but linearly independent in C[1,1].
Prove that in a given vector space V, the zero vector is unique.
Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that among all the scalar multiples cv of the vector v, the projection of u onto v is the closest to u that is, show that d(u,projvu) is a minimum.

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Exercise 3.1.4. The set of all twice differentiable functions f for which f"(x) +2f(x) = 0 holds.