11. Fix some positive integer n, and some a € R. The setW = {ƒ € P₂(R) | ƒ(a) = 0}is a subspace of P₁ (R), the space of polynomials with real coefficients ofdegree ≤n. (You do not need to prove this.) Determine the dimension of W.

The given subspace .The objective is to find the dimension of the subspace .

Answered: 11. Fix some positive integer n, and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

19. Let F be the set of polynomials in P(IR) that are divisible by x2 - 9 and G the set of polynomials in Pa(R) that are divisible by x – 27. Prove that F and G are subspaces of P4(R) and find their dimensions. Also find dim(FnG) and dim(F+ G).
Which of the following sets are subspaces of R³? A. {(x, y, z) | 2x − 8y + 3z = 9}| B. {(−5, y, z) | y, z arbitrary numbers }| c. {(-9x, -2x, 8x) 1 x arbitrary number} D. {(x, 0, 0) 1 x arbitrary number}| E. {(x, y, z) | − 5x + 4y + 7z = 0}| - F. {(x, y, z) x
Q2. Let V be a vector space over a field (F, +, .), let M1 , M2 and M3 be subspaces of V. Prove or disprove that M1NM20M3 is also a subspace of V.
4. Let H be the set of 2 x 2 whose trace is equal to zero. That is -o} A11 a12 H = E M2(R) | a11 + a22 = A21 A22 Prove that H is a subspace of M2(R).
Please show work
Please Help!
20. Let f be a continuous linear functional defined on the normed linear space X. Show that M = {xe X\f(x) = 0) is a closed subspace of X.
For each of the sets below, determine if the set is a vector space or subspace. a. H = {2], a, b real} а. b. V = , а — b {E 1.a, b real} С. T= 0 b. C = {the set of all complex numbers of the form a + bi, where a, b are real} e. J= {the set of all polynomials such that p(t)divides evenly by (t – 1)} [Hint: write p(t) in factored form, with the factor (t – 1) pulled out. What does the other factor look like?] d. - {the set of all odd functions: f (-x) = -f(x)} W is the set of all nxn matrices such that A² = A. h. Q is the set of all exponential functions i. f. g. S is the set of all n x n singular matrices
Select ALL sets that are not subspaces of R². The set containing the points on the graph of the line y = 2x – 13. The set R². The set {[_²2,3]} 13 The set containing all multiples of [ 2.83] 13 The set The set containing the points on the graph of the line y = {[:]}. 2 13 x.
Determine if the given set is a subspace of the appropropriate R^n and justify your conclusion.
'

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

11. Fix some positive integer n, and some a E R. The set {ƒ ≤ P„(R) | ƒ(a) = 0} W = is a subspace of Pn (R), the space of polynomials with real coefficients of degree ≤n. (You do not need to prove this.) Determine the dimension of W.