2) The speeds of oscillation, x, of a loaded beam is given by the equation: x³ 3.25 x² + x -0.063 = 0 Determine the positive value (root) of .x which is between (2) and (3), by use bisection method. a) x₂ = 3.75 b) x₂ = 1.75 c)x₂ = 2.75

(B. Janssen, KTH, 2014) Consider the linear system 0.550x+0.423y = 0.127 0.484x + 0.372y = 0.112 Suppose we are given two possible solutions, u = [_11] and v- -1.91. 1.01 0.9 a. Decide based on the residuals b - Au and b - Av which of the two possible solutions is the 'better' solution. b. Calculate the exact solution x. c. Compute the errors to the exact solution. That is, compute the infinity norms of u-x and v-x. Do the results change your answer to 7a?

Q1: Use the Jacobi method to find four iterations of the following system of linear equations 5x1 – 2x2 + 3x3 = -1 -3x + 9x2 + x3 = 2 2x, - x2-7x3 = 3 Using initial approximation(x,, x2, X3) = (0,0,0).

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Q. 6. (b) Describe Newton Raphson method for solving the system of non-linear equation. Use NR method to find roots of the equation T

(3). Use the Gaussian elimination and four-digit rounding arithmetic to solve the following linear system and compare the approximation to the actual solution. J0.03001r1 + 58.81r2 = 59.11, 5.310r1 - 6.101r2 = 47.00. The actual solution is [10, 1].

Consider the following system of equations in R2→R? y + 2x + x – yıy2 = 15 2y + xỉ + x + yıY2 = 38 What is the value of y, and y2 if x1 = 1 and x2 : = -1 By using derivative, calculate the new value of y, and y2 when x1 reduces

Slove the equation fcx) = x²- 3 X +1 Stark Xo=3 use Interation Method

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4. Consider T(r1,12, 13) = (3r1 – 212 + 4r3, I1 + 2r3, 12). Find T-. %3D