(6) (a) Use the software for solving linear systems that was introduced in the recitation to solve the linear system, Ax = b, and estimate the condition number of A, where [0.1 0.2 0.3 A= 0.4 0.5 0.6 b = [0.1] 0.3 ' 0.7 0.8 0.9 0.5 (b) What is the estimate of Cond(A)? Based on the size of the condition number, how would you describe the linear system? (c) How many digits of accuracy do you expect the computed solution to have? Justify your answer. Note that this computation is performed using single precision arithmetic.
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- 5(More in the next set.) (a) Verify that the given functions are linearly independent and form a basis of solutions of the given ODE. (b) Solve the IVP. Graph or sketch the solution. 15. 4y" + 25y = 0, y(0) = 3.0, y'(0) = -2.5, cos 2.5.x, sin 2.5xYou solve a non-singular system of 1,000 linear equations with 1,000 unknowns. Your code uses the Gauss-Jordan algorithm with partial pivoting using double precision numbers and arithmetics. Why would the 2-norm of the residual of your solution not be zero?
- ignore " Then use Theorem 3.3 in theBurden & Faires textbook to find an error bound for the approximations you obtained but do the rest please with the proper steps and please do not use chat gpt! Thank you !Please no written by hand solutions Numerical Methods(Numerical analysis) Here’s a challenging problem for those who know a little calculus. The Newton-Raphson method can be used to find the roots of any equation y(x)=0. In this method, the (i+1)stapproximation,xi+1,toarootofy(x)=0 is given in terms of the ith approximation, xi, by the following formula, where y’ denotes the derivative of y(x) with respect to x: xi+1=xiy(xi)/y(xi) For example, if y(x)=3x2+2x2,theny(x)=6x+2 , and the roots are found by making a reasonable guess for a first approximation x1 and iterating by using this equation: xi+1=xi(3xi2+2xi2)/(6xi+2) a. Using the Newton-Raphson method, find the two roots of the equation 3x2+2x2=0. (Hint: There’s one positive root and one negative root.) b. Extend the program written for Exercise 6a so that it finds the roots of any function y(x)=0, when the function for y(x) and the derivative of y(x) are placed in the code.
- Consider the system of linear equations X2 + 2x3 X4 -1 X1 X2 X3 -X1 X2 + X3 + 3.x4 1 - Xị + 2x2 X4 9 Use Matlab to find the LU decomposition of the coefficient matrix A and then solve the resulting triangular system using forward and backward substitutions programs. (You need to provide the codes)Please solve.An aluminum wire having a cross-sectional area equal to 4.60 x 10-6 m? carries a current of 7.50 A. The density of aluminum is 2.70 g/cm³. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire. 1.95E-4 The equation for the drift velocity includes the number of charge carriers per volume, which in this case is equal to the number of atoms per volume. How do you calculate that if you know the density and the atomic weight of aluminum? mm/s
- V Obtain the expression for y(t) which is satisfying the differential equation ÿ + 3y+ 2y = et y(0)=0 and y(0)=0For an object of mass m=3 kg to slide without friction up the rise of height h=1 m shown, it must have a minimum initial kinetic energy (in J) of: h O a. 40 O b. 20 O c. 30 O d. 10(a) For which bases b is (14641)b the fourth power of an integer? (b) Find the base b if (62)b \times (11)b (1012)b. (c) Find a base b in which (45)b and (55)b are squares of consecutive integers. (d) Find x if (2x 3)4 = (1x10)3 =