APPLIED NUMERICAL METHODS WITH
PYTHON FOR ENGINEERS AND SCIENTISTS
EXAM SCRIPT SOLVED QUESTIONS
ACCURATE ANSWER COLLECTION
●● What are the two common methods for solving simultaneous
equations?
Answer: Elimination of unknowns and the use of determinants (Cramer's
rule).
●● What is a significant drawback of using Cramer's rule for large
systems?
Answer: It requires (n - 1)(n + 1)! multiplications, which is impractical
for large n.
●● What is the general form of a set of linear algebraic equations?
Answer: a11x1 + a12x2 + ... + a1nxn = C1, ..., an1x1 + an2x2 + ... +
annxn = Cn.
●● What defines a nonhomogeneous set of equations?
Answer: If the values of C's are not all zero and all equations must be
independent for a unique solution.
,●● What defines a homogeneous set of equations?
Answer: If all values of C's are zero, and a non-trivial solution exists
only if not all equations are independent.
●● What is the Direct Method for solving linear equations?
Answer: It includes methods like Gauss Elimination, Gauss-Jordan
Elimination, LU Decomposition, and Matrix Inversion.
●● What is the Indirect Method for solving linear equations?
Answer: It includes iterative methods such as Jacobi Iteration, Gauss-
Seidel, and Successive Over Relaxation (SOR).
●● What is a matrix?
Answer: A rectangular arrangement of numbers represented by a single
symbol with n rows and m columns.
●● What is a row matrix?
Answer: A horizontal set of elements in a single row, e.g., a 1 x m
matrix.
●● What is a column matrix?
Answer: A vertical set of elements in a single column, e.g., an n x 1
matrix.
, ●● What is a square matrix?
Answer: A matrix where the number of rows equals the number of
columns (n = m).
●● What is a symmetric matrix?
Answer: A matrix where aij = aji for all i and j.
●● What is a diagonal matrix?
Answer: A square matrix where all elements of the main diagonal are
non-zero and all other elements are zero.
●● What is an identity matrix?
Answer: A diagonal matrix where all elements on the main diagonal are
equal to 1.
●● What is an upper triangular matrix?
Answer: A matrix where all elements below the main diagonal are zero.
●● What is a lower triangular matrix?
Answer: A matrix where all elements above the main diagonal are zero.
●● What is a banded matrix?
PYTHON FOR ENGINEERS AND SCIENTISTS
EXAM SCRIPT SOLVED QUESTIONS
ACCURATE ANSWER COLLECTION
●● What are the two common methods for solving simultaneous
equations?
Answer: Elimination of unknowns and the use of determinants (Cramer's
rule).
●● What is a significant drawback of using Cramer's rule for large
systems?
Answer: It requires (n - 1)(n + 1)! multiplications, which is impractical
for large n.
●● What is the general form of a set of linear algebraic equations?
Answer: a11x1 + a12x2 + ... + a1nxn = C1, ..., an1x1 + an2x2 + ... +
annxn = Cn.
●● What defines a nonhomogeneous set of equations?
Answer: If the values of C's are not all zero and all equations must be
independent for a unique solution.
,●● What defines a homogeneous set of equations?
Answer: If all values of C's are zero, and a non-trivial solution exists
only if not all equations are independent.
●● What is the Direct Method for solving linear equations?
Answer: It includes methods like Gauss Elimination, Gauss-Jordan
Elimination, LU Decomposition, and Matrix Inversion.
●● What is the Indirect Method for solving linear equations?
Answer: It includes iterative methods such as Jacobi Iteration, Gauss-
Seidel, and Successive Over Relaxation (SOR).
●● What is a matrix?
Answer: A rectangular arrangement of numbers represented by a single
symbol with n rows and m columns.
●● What is a row matrix?
Answer: A horizontal set of elements in a single row, e.g., a 1 x m
matrix.
●● What is a column matrix?
Answer: A vertical set of elements in a single column, e.g., an n x 1
matrix.
, ●● What is a square matrix?
Answer: A matrix where the number of rows equals the number of
columns (n = m).
●● What is a symmetric matrix?
Answer: A matrix where aij = aji for all i and j.
●● What is a diagonal matrix?
Answer: A square matrix where all elements of the main diagonal are
non-zero and all other elements are zero.
●● What is an identity matrix?
Answer: A diagonal matrix where all elements on the main diagonal are
equal to 1.
●● What is an upper triangular matrix?
Answer: A matrix where all elements below the main diagonal are zero.
●● What is a lower triangular matrix?
Answer: A matrix where all elements above the main diagonal are zero.
●● What is a banded matrix?
