I The function gaussElimin also works with complex numbers. Use it to so Ax = b, where
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I'm curious about how to solve the problem and the Python code.
![Problem 2.6 (Gauss elimination for a compler linear system)
I The function gaussElimin also works with complex numbers. Use it to solve
Ax = b, where
5+ 2i -5+3i 6– 3i
8 - i
-3 – 3i
5+i
5+ 2i
7- 2i
-1+3i
-5+ 3i
8 - i
2+ 2i
6 – 3i -1+3i
2+ 2i
8+ 14i
b =| 15 – 35i 2+ 10i -2-34i 8+14i
]"](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4c8aec3-b81d-4a96-b363-33d225d647f6%2F76dc72ea-2422-40e4-b13d-e20d0d33b81a%2Fmv7qpdw_processed.jpeg&w=3840&q=75)
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- olve the following initial value problems for the systems of equations using the matrix method. Findeigenvalues and eigenvectors and fix the undetermined coefficients by using technology (for example,Matlab or WolframAlpha)(a)x′ = x + 2y + 2zy′ = 2x + 7y + zz′ = 2x + y + 7z, x(0) = 9, y(0) = 1, z(0) = −1.(b)x′ = 9x − 7y − 5zy′ = −12x + 7y + 11z + 9wz′ = 24x − 17y − 19z − 9ww′ = −18x + 13y + 17z + 9w, x(0) = 2, y(0) = 0, z(0) = 1, w(0) = 14 We consider the following initial value problem for two functions y(x),z(x): 0=y′′+(y′+6y)cos(z), 5z′=x^2+y^2+z^2, where 0≤x≤2 and y(0)=1.7, y′(0)=−2.7, z(0)=0.5. Approximate the solution of this initial value problem using Euler's method with 100 steps. (use Maple) What approximation value do you obtain for y(2) and z(1)?Problem 2:Use Newton’s method to find the root of f(x) = x3 − 9, with starting point x0=2 and tolerance error to be 0.00001 solve in python plz
- Using MATLAB, develop a computer program for the finite difference solution with general θ scheme for the 1D consolidation of a uniform layer of soil. Compare the results for θ=0, 0.5, 2/3 and 1.0 for α=0.49 and α=0.51 against the analytical solution of Terzaghi’s equation for T=0.5. Apply the program to both cases of double draining layer and single draining layer.Electromagnetic Pulse propagating at oblique angle to a dielectric interface Consider a gaussian wave pulse propagating along the z-axis from region 1 with refractive index n1 and onto a dielectric interface y = m z (for all x). To the left of this dielectric interface, the refractive index is n2. Devise an initial value computer algorithm to determine the time evolution of the reflected and transmitted electromagnetic fields for this pulse. e.g., n1 = 1 , n2 = 2 initial profile (t = 0, with z0 < 0) Ex = E0 exp[-a (z-z0)^2] By = n1 * Ex Choose parameters so that the pulse width is at least a fact of 8 less than the z- domain of integration ( -L < z < L). For the slope of the interface, one could choose m = 1.I'm having trouble understanding what exactly makes a linear ordinary differential equation "linear". I know that the major advantage of the linear ODEs is that a linear combination of particular solutions gives another particular solution. Characterized by additivity and homogeneity, this means that the output for a sum of inputs is equal to the sum of outputs for each individual input (e.g., f(3) + f(5) = f(3+5)= f(8)) and scaling the input by a factor scales the output by the same factor (e.g., f(6x) =6f(x)...but how would this look? Like say if I had 4e^5(t-1) satisfying the differential equation dy/dt=5y where y(1)=4, what would that "linear combination" look like?
- Solve the following system of equations using Gauss/Gaussian Elimination method. 2x + 4y + 2z − 3v − 2w = 23x − 3y + 2z − v = 133x + 5y − v = 10x + 7y + 9z = 152x − 7z − 3v − 3w = 9I want the solution for problem 1, 2 and 32. Heat conduction in a square plate Three sides of a rectangular plate (@ = 5 m, b = 4 m) are kept at a temperature of 0 C and one side is kept at a temperature C, as shown in the figure. Determine and plot the ; temperature distribution T(x, y) in the plate. The temperature distribution, T(x, y) in the plate can be determined by solving the two-dimensional heat equation. For the given boundary conditions T(x, y) can be expressed analytically by a Fourier series (Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 1993):
- Given the following Boolean function with “don’t care” terms, use a 4-variable Karnaugh map to simplify it in product-of-sums form. h(w, x, y, z) = Sm(0, 1, 8, 9, 11, 12, 13, 14) + D(2, 10, 15)1. Determine the equation of the line through the given point (a) parallel and (b) perpendicular to the given line Given: Point: ( -1,-4) Line: 4x-2y=3 2. Draw the line 4x-2y=3 and your answer for letter (a) in problem number 1 3. Draw the line 4x-2=3 and your answer for letter (b) in problem number 1 4. a2x-7ay+5a=0 Reduce the given equation to (a) intercept form (b) slope-intercept form A is the last two digit of your ID number, for example your ID number 20201000111, then (a) is 11 hence your equation would be 22x-77y+55=0This solution seems confusing. Please give the correct solution for this problem!!!!
