(7) In the ring (Z, +, .), we get n {P:P non trival prime ideal in Z}: (a) o (b) (Z, +, .) (c) ({0},+,.) (d) No Choice
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- 1. Find the natural cubic spline sN (x) passing through the 3 points (xj, yj) given by (0, 2), (2, 3), and (3, 1).Then evaluate sN (1).true or false In the domain of Gaussian integers Z[i], the element 17 is IrreducibleQ2. (a) Show that \{e ^ (- x), x * e ^ (- x)\} is a fundamental set of solutions of y^ prime prime +2y^ prime +y=0 on(0, ∞)
- Find a polynomial of degree n=4 that has the given zero(s) x = −4, −1Consider the ODE eigenvalue problem: ((1-x2)1/2φ')' + λ(1-x2)-1/2φ = 0 posed for -1 < x < 1 and subject to the boundary condidiont |φ(-1)| < ∞ and |φ(1)| < ∞. If you find it helpful you, you may assume |φ'(-1)| < ∞ and |φ'(1)| < ∞. a) Show that this is a Sturm-Liouville eigenvalue problem, i.e, verify that it has the correct form and identify the coefficients p, q, and σ. Is the problem regular? Why or why not? b) Show that λ > 0 for each eigenvalue λ.How can I find all monic divisors of degree 1 in Z_7 [x], 5x^2+5x+4? please help me get started with this problem.
- is x^3 + 1 irreducible over Z_3?Consider the following system of equations over the finite field Z3 x + 2y + z = 1x + z = 1x + y + z = 1 (a) What is the reduced row echelon form of the associated augmented matrix? Write down the sequence of operations you performed to obtain the reduced row echelon form. (b) Describe the solution set and state how many different solutions are there.Prove that (1,1) is an element of largest order in Zn1 + Zn2. State the general case. Needs Complete solution with 100 % accuracy.
- For the part highlighted in green, why doesn't negative infinitiy cancel with the negative near the x, and give us infinity? Instead it gives us 0. I know a number to thr negative infinity power is 0, just thought 2 negatives made a positive so was wondering why not here. And also, would thus converge or diverge?Find z1 and z2. use gauss elimination, not gauss jordangeneral solution of the PDE uux + yuy = x is of form