1. Using Gaussian Elimination method to solve the following system of linear equations: [CLO1:C3] [8 marks] 2x1+4x2-3x3 = -17 x1-2x2+x3 = 12 5x1+x2-4x3 = -7 2. Use the fixed-point iteration method to find the root of 3x - e<sup>x</sup> = 0. Give your answers correct to 3 decimal places. [CLO1:C3] [7 marks] 3. Form the Order Differential Equations for y = Ae<sup>3x</sup> - Be<sup>3x</sup>. [CLO1:C2] [4 marks] 4. Solve the following Order Differential Equations. i. \frac{dy}{dx} = \frac{y^2+x^2}{2xy} [CLO2:C2] [7 marks] ii. 5\frac{d^2y}{dx^2} - 27\frac{dy}{dx} - 18y = 0 [CLO2:C2] [4 marks]
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Solving the system of linear equations using Gaussian Elimination method: Step 1: Write the augmented matrix for the system of equations: [4 -2 3 | 5] [2 3 -4 | -7] [3 -5 2 | 9] Step 2: Perform row operations to get zeros below the main diagonal: R2 = R2 - Show more…
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