EIT Computer Science and Numerical Methods 2

Question 1

Gaussian elimination is used to solve:

Accepted Answer

Systems of linear algebraic equations

Answer

Gaussian elimination uses elementary row operations to reduce a linear system to upper triangular form for back-substitution.

Question 2

What is the hexadecimal equivalent of decimal 255?

Accepted Answer

FF

Answer

255 = 15×16¹ + 15×16⁰ = FF in hexadecimal.

Question 3

Euler's method for solving ODEs advances the solution using:

Accepted Answer

A forward difference approximation of the derivative

Answer

Euler's method uses yₙ₊₁ = yₙ + h·f(xₙ, yₙ), a first-order forward difference step.

Question 4

A high condition number for a matrix indicates that the corresponding linear system is:

Accepted Answer

Numerically ill-conditioned and sensitive to perturbations

Answer

A high condition number means small changes in the input data cause large changes in the solution.

Question 5

Among bisection, false position, secant, and Newton-Raphson methods, which converges fastest near a simple root?

Accepted Answer

Newton-Raphson method

Answer

Newton-Raphson achieves quadratic (second-order) convergence, doubling correct digits each iteration.

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