18. If F is a field and I is the ideal (x2,xy) in F[x,y), then there are at least three dis-tinct reduced primary decompositions of I; three such are:(i) 1 = (x) N (x*,y); (ii) I = (x) N (x?,x + y); (iii) I = (x) N (x*,xy,y9.

Given: Let's consider F be the field and I be the x2,xy in Fx,y, then the distinct reduce primary…

Answered: 18. If F is a field and I is the ideal…

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

6. 'The mapping T :R³ → R² is defined as T (x, y, z) = (x + 2y+ 3z, x + 3y + 2z) is a linear transformation from R³ into R². Then %3D its Kernel T is (a) L {c} where a = (- 1, 5, 1) (b) L{a} where a = (- 1, 1, 5) (ç) L{a} where a = (- 5, 1, 1) (d) None of these
1. Find curl(v) of the following in terms of (x1, x2, x3) and (e1, e2, e3). If curl(v) = 0, find the function f such that Vf = v. a. v(x) = (x² + x + x3)-'(x1e1 + x2€2 + X3@3). b. v(x) = (xỉ + X2X3)e1 + (x3 + X1X3)e2 + (xž + x2X1)e3 c. v(x) = e"1(sin(x2) cos(x3)e1 + sin(x2) sin(x3)e2 + cos(x2)e3)
17. Find ø if (a) Vø = (y² – 2xyz³)i+ (3+ 2xy – x²2³)j+ (4z³ – 3x²yz²)k and ø(1, 1, – 1) = 4. (b) Vø = 2xyz³i+x²z³j+ 3x²yz²k and ø(1, –2, 2) = 4.
+ ceit I R L,e,R real Core Enpress e in form of Aeio write value s ef A, O
If the characteristic polynomial of the system r"= AY is given by P(r)3(+1)r-1) Then 2.4 +1 equals to a) 1 b) 0 c) -31 d) 31
2. (a) Show that the polynomials p, (x)=1+x, p,(x)=1+2.x – x², p;(x)=x+x² are linearly independent. (b) Decide if polynomial q(x)=-1+x is in the span{p, (x), P2 (x), P;(x)} .
12. Let B = {1+2x, x - x²,x + x²}. (a) Show that B is a basis for P2. (b) Let p(x) = 1+ 3x + x². Compute the coordinate [p(x)]g of p(x).
5. Find two linearly independent polynomials orthogonal to p(x) = 1 + x² using the inner product from problem 2.
Question 2 dependent in P[r]. Prove that the polynomials r2+2r-1, x²+1 and x² + are linearly
4. Let S E L(P3(R), P3(R)) be defined by S(p(x)) = xp'(x). Find a basis for null(S). Is S injective?

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

18. If F is a field and I is the ideal (x,xy) in F(x,y), then there are at least three dis- tinct reduced primary decompositions of I; three such are: (i) 1 = (x) N (x²,y); (ii) I = (x) N (x²,x+ y); (iii) I = (x) N (x²,xy,y?). %3D