EIT Computer Science and Numerical Methods 3

Question 1

Gaussian elimination is a direct method for solving:

Accepted Answer

Systems of linear algebraic equations

Answer

Gaussian elimination reduces an augmented matrix [A|b] to upper triangular form through row operations, then back-substitutes to find the solution vector.

Question 2

Using 8-bit two's complement representation, the range of signed integers is:

Accepted Answer

-128 to 127

Answer

With 8 bits in two's complement, the most negative value is -128 (10000000) and the most positive is 127 (01111111).

Question 3

The central difference approximation for the second derivative f''(x) is:

Accepted Answer

[f(x+h) - 2f(x) + f(x-h)] / h²

Answer

The second-order central difference formula for f''(x) combines f at x+h, x, and x-h with coefficients 1, -2, 1 divided by h².

Question 4

For the bisection method to guarantee finding a root on interval [a, b], which condition must hold?

Accepted Answer

f(a) · f(b) < 0 (the function changes sign over the interval)

Answer

By the Intermediate Value Theorem, if f is continuous and f(a) · f(b) < 0, then at least one root must exist between a and b.

Question 5

In object-oriented programming, inheritance primarily allows:

Accepted Answer

A subclass to acquire the methods and attributes of a parent class

Answer

Inheritance creates an is-a relationship where the child class automatically gains all accessible members of the parent, enabling code reuse.

EIT - Engineering in Training Practice Test

EIT - Engineering in Training Practice Test

EIT Computer Science and Numerical Methods 3