Find 0 (t) where 0 (t) = 0 + Ot. B
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![Find [0 (t)]
where 0 (t) = 0 + Ot.
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- Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2What is the coefficient of x^n for the generating function (1)/(1+x)^2?Let P3(x) be the interpolating Lagrange polynomial of degree 3 passing through the points (0,0),(1/2, y), (1,3) and (2,2). If the coefficient of x3 in P3(x) is 6, then determine the value of y.
- 1. Suppose that the solution of a homogeneous linear ODE with constant coefficients is y=c1+c2e-t+c3te-t+c4e-tcos(3t)+c5e-tsin(3t). a. what is the order of the ODE? b. What are the roots (with multiplicities) of the characteristic polynomial? c. What is an ODE which has this solution?a) Show that the cubic polynomials P(x) = 3 − 2(x + 1) + 0(x + 1)(x) + (x + 1)(x)(x − 1) and Q(x) = −1 + 4(x + 2) − 3(x + 2)(x + 1) + (x + 2)(x + 1)(x)both interpolate the data x −2 −1 0 1 2 f(x) −1 3 1 −1 3Find the string that has this generating function: a) (1− x)−3b) (1+2x)−4c) 1/(1 −3x)3d) 1/(1+ x)2e)1/ (1− 2x)2
- consider the function y=ax2+bx+c, where a is in the set {n∈ℕ|(n|15)}, b is an integer less than 10, and c is a prime less than 20. how many second degree polynomials can we make in the form y=ax2+bx+c, where a,b,and c are in the given sets?This is a question from a linear algebra course: Let V = R[X]3, the polynomials of degree at most three, and B = {1, X, X2, X3}. Show what the image under fB is of:• the four basic elements: P1(X) = 1, P2(X) = X, P3(X) = X2 and P4(X) = X3• P(X) = 2 + 6X + 3X2 + 4X31) consider the degree 4 LFSR given by polynomial p(x)=x^4+x^2+1. What kind of polynomial is this p(x)=?
- 1. Find the values of w, x, y and z in fraction form using (a)Gauss Elimination, (b)Gauss-Jordan Elimination and (c)Cramer's Rule. 8w - 5x + 9z - 2y = 5 2x + 8z + 2y = 3 7z - 6w - 8x + 4y = 3 w + 5x + 2z = 1Suppose A ∈ Rm×n (m ≥ n) has full rank. Show that the reduced QR factorization A = QˆRˆ (with the diagonal entries of Rˆ to be strictly positive) is unique.H 5. Write down all normalized polynomials of degree at most 4 in Z_2[x]. Underline the reducible polynomials
