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- Solve for the value of x, y, and z using Gauss-Jordan Method.solve for w,x,y,z using Gaussian eliminationConsider the homogeneous CLTI system ?̇ = ?? where? = H2 1 00 −1 2−1 0 1I.a) Is ? diagonalizable? If not, find its Jordan normal form.b) Find the matrix exponential ?KL (using the Jordan form) and the analytical solution of ?(?) forarbitrary initial condition ?N.
- For the following matrix: a) find the eigenvalues and the eigenvectors b) check the answer by using the orthogonal property (x(i))T(x(j))=1(i≠l) c) determine the three normalized eigenvectors by using (x(i))T(x(i))=1(i≠l)The initial value problem [dxdtdydt]=[−53−4−2][xy], x(0)=1,y(0)=−1 is to be solved on the interval t∈[0,1] using the backward Euler method with step h=0.05 The iteration update rule for the method is [xn+1yn+1]=(I−hA)−1[xnyn], where I is a 2×2 identity matrix. Determine the approximate values of x(1)= ?(round to the fourth decimal place) and y(1)= ? (round to the fourth decimal place). Now use the Matlab solver ode45 to obtain the solution at t=1: x(1)= ? (round to the fourth decimal place) and y(1)= ? (round to the fourth decimal place).Q2) for the following Matrix ‘A°, Please determine the following: a. Eigenvalue of A b. Eigenvector of A, make your answer for a. and b, in the unit vector form.
- You have a nonlinear model to fit to data, with two parameters a and b. Taking the derivative of theerror function with respect to a and b led to F and G functions as given below:F(a, b) = ab – a2G(a, b) = ab + bNewton-Raphson formula for iteration . The initial point for the iteration is given as Z0 = (1 1)Apply the Newton-Raphson formula to calculate Z1.For Jacobian matrix calculation, use numerical derivativeapproach.For an auditorium: Room condition: 26oC DPT, 19 oC WPT; Outside conditions: 35 oC DPT 27 oC WPT; Room heat gains: Sensible heat= 11.1 kW Latent Heat= 3.9 kW The conditioned air supplied to the room is 50 cm/min and contains 25 percent fresh air and 75 percent re-circulated room air. Determine; a) The DBT and WBT of supply air. b) The DBT and WBT of mixed fresh and re-circulated air before the cooling coil. c) The apparatus due point in bypass factor of the coil d) The refrigeration load on the cooling coil and the moisture removed by the coil.Solve for the integrating factor of the D.E
- Let B be a matrix which has eigenvectors u1 = (1 1 0 ), u2 = (1 −1 0 ), and u3 = ( 0 0 1 ), with corresponding eigenvalues λ1 = 2, λ2 = .5 and λ3 = −3. Compute B4x, where x = (3 5 −3 ). (hint : you do not need to calculate the matrix B explicitly)Consider the followiing equation (t^2)y′′−6y =0, t > 0, check that y1 =t^3 and find y2 and write the solution of y(t) Choose your favorite method to find the second linearly independent solution (Abel's theorem or reduction or order). Choose the correct form of the general solution from the list below.Suppose that all the eigenvalues of the matrix A have negative real part. Then everysolution of the differential equation x`= Ax satisfies,|x(t)| ≤ |x(s)|, if t > s.