1. In the following item a field K and a complex number a is given. Find theminimal polynomial of a and the degree of a over K.Oa. K = Q.a =√3+1.b. K=Q, a = √2 + √/2.c. K = Q, a = 1 but a / 1.d. K = Q(√-1), a = √2.e. K = Q(√2), a = √2.f. K = Q, a = 1 but a # 1, p is prime.

According to bartleby guidelines we do only first three subparts and rest part can be reposted…

Answered: 1. In the following item a field K 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

Solve the following problems and show your complete solutions. Write it on a paper and do not type your answer.
1. Find the locus of the equation /z-2+4j/=3/z/ and state the shape 2.using demoivre principle expand (1/2 + j√3/2)¹³ 3.find the root of the polynomial given that one of the root is 2i in x⁴+x³+5x²+4x+4=0
Consider the proof below of the fact that I + a = 1 + b iff a - bEI where R is a commutative right with unity and I is an ideal. Identify which “+" signs are notation and which "+" signs are operations. (=) Assume I + a = 1 + b. : a E l + a : a el + b . a = i+ b for some i EI : i = a – b i a – b E l (=) Assume a – b E I Assume ΧΕ α :x = i + a for some i E I :x = i+ a + (-b+ b) :x = (i + a - b) + b i x E I + b : I + a CI+ b Assume x E I+ b :x = i + b for some i El :x = i +b+ (-a + b) : x = (i + b – a) + a : x € l + a :I+b SI+a : I+ a = 1 + b Consider the proof above and justify each claim.
1.F.3 One of my favorite bases of P<4 is X = {1,x,2x² – 1,4x3 – 3r, 8x“ – 822 + 1}. Find the coordinates of 1, x, x², x³, and xª with respect to X. Aside: These polynomials are called Chebyshev polynomials (of the first kind). You may remember your trig identity cos(26) = 2 cos²(8) – 1. If x = cos(0) then cos(20) = 2x² – 1. Similarly, cos(30) = 4.x3 – 3x and cos(40) = 8x4 – 8x² +1. So, when you found the coordinates of x4 above, you secretly found a way to write cos (0) as a linear combination of {1, cos(0), cos(20), cos(30), cos(40)}.

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

1. In the following item a field K and a complex number a is given. Find the minimal polynomial of a and the degree of a over K. O a. K = Q.a = √3+1. b. K=Q, a = √2 + √/2. c. K = Q, a = 1 but a / 1. d. K = Q(√-1), a = √2. e. K = Q(√2), a = √2. f. K = Q, a = 1 but a # 1, p is prime.