2. Show how to derive the last 4 rows of the polynomials over GFI2) (in alphal we went over in cl...
Preview Activity 14.1. In previous investigations, we defined irreducible polynomials and showed that irreducible polynomials in polynomial rings over fields play the same role as primes play in Z. In this investigation we will explore some methods to determine when a polynomial is irreducible, with a special emphasis on polynomials with coefficients in C, R, and Q. To begin, we will review the definition and a simple case. Let F be a field. (a) Give a formal definition of what...
Show that the following polynomials are irreducible over Q. (a) (8 points) f(1) = 5.rº – 1826 + 30x4 – 6r2 + 12x + 60 (b) (12 points) g(x) = r" - 6.12 – 4.: +3
Problem No. 2 (28 pts) Solve the polynomials and show only the real solutions. (4-Digits) x47 2.2 f()2x +23x 2.3 f(x) = x8 + x2-391 2.4 f(x)-(230.5)x3-x
I am confused about how to solve (b) (c) (d)
(4) (Interpolating polynomials) Say we want to find a polynomial f(x) of degree 3, satisfying some interpolation conditions. In each case below, write a system of linear equations whose solutions are (ao, a1, a2, az). You don't need to solve. (a) We want f(x) to pass through the points(1,-1), (1, 2), (2,1) and (3,5). (b) We want f(x) to pass through (1,0) with derivative +2 and (2,3) with derivative-1 (c)...
1. Show how to derive the IS curve as we specified in the class. Show all the necessary steps (from the very beginning) to derive the IS curve. Draw a graph of the IS curve as well. What is the slope of the IS curve? What's the intuition of the sign of slope (positive or negative)? Explain clearly. 2. Analyzing macroeconomic events with the IS curve: consider the following events in the macroeconomy. Show how to think about them using...
7. (16 pts.) We are given a 4 x 4 matrix A, with rows r1,..., r4. The matrix B is obtained from the rows of A as described below: 12 A= B 4r + ri +2r3 2r2 + 4r r3 +r2 3r1 13 TA How are the determinants of A and B related?
Find the missing line and angle of D? My professor went over
thus very short over class. We are supposed to plot each line given
on an index card on a coordinate plan and find the missing degree
and length of D. Im very confused. The whiteoff
board is his exmple..
Thank you
2-AMPER coMT GN) 100 A /50 xXX +81.0 TANO- X R-lenjie di A 00 ి 270 ఉO • 150 డ - 200
1. Let Q be the set of polynomials with rational coefficients. You may assume that this is an abelian group under addition. Consider the function Ql] Q[x] given by p(px)) = p'(x), where we are taking the derivative. Show that is a group homomorphism. Determine the kernel of 2. Let G and H be groups. Show that (G x H)/G is isomorphic to H. Hint: consider defining a surjective homomorphism p : Gx HH with kernel G. Then apply the...
3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using the orthogonality relation f P(x)Pm(x)dx = 0, mn and m,n E N. 1 and P1(x) = x be two Legendre polynomials of degree 0 and 1,
3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using the orthogonality relation f P(x)Pm(x)dx = 0, mn and m,n E N. 1 and P1(x) = x be two Legendre polynomials of...
In Module 2 we went over gross domestic product and gdp per capita. Compare your current standard of living with that of your parents. Ask them or somebody you know around their age to recall where they were living, what they owned and if available how much (a price) something cost them then (house, car, their wage). What has happened to the average standard living over the past 30+ years? Be sure to include examples from your conversation.