Exams › GATE › Engineering Mathematics

Solution of the variables x1 and x2 for the following equations is to be obtained by employing the Newton-Raphson iterative method. equation (i) 10x2 sin x1 - 0.8 = 0 equation (ii) 10x2² - 10x2 cos x1 - 0.6 = 0 Assuming the initial values x1 = 0.0 and x2 = 1.0, the Jacobian matrix is

1. [10 -0.8; 0 -0.6]
2. [10 0; 0 10]
3. [0 -0.8; 10 -0.6]
4. [10 0; 10 -10]

Correct answer: [10 0; 0 10]

Solution

J = [[10 x2 cos x1, 10 sin x1],[10 x2 sin x1, 20 x2 - 10 cos x1]]. At x1=0, x2=1 this gives [[10,0],[0,10]] (idx 1). The stored idx 2 [0 -0.8; 10 -0.6] is wrong.

Related GATE Engineering Mathematics questions

• The smallest positive root of the equation x⁵ - 5x⁴ - 10x³ + 50x² + 9x - 45 = 0 lies in the range
• For a flowing fluid, a dimensionless combination of velocity (V), length scale (l), and acceleration due to gravity (g) would be
• The second derivative of a function f is computed using the fourth-order Central Divided Difference method with a step length h. The CORRECT expression for the second derivative is
• In the IEEE floating point representation the hexadecimal value 0x00000000 corresponds to
• Let r denote number system radix. The only value(s) of r that satisfy the equation √121_r = 11_r, is/are
• The Newton-Raphson iteration xₙ₊₁ = 1/2 (xₙ + R/xₙ) can be used to compute the

⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →