D420 Discrete Math: Functions and Relations - Set 5 - Part 3

Test your knowledge of technical writing concepts with these practice questions. Each question includes detailed explanations to help you understand the correct answers.

Question 41: Which of the following is true for a square matrix to be invertible?

It must have a non-zero determinant

It must have a zero determinant

It must have no rows or columns of zeros

It must be symmetric

Question 42: Which of the following best describes a singular matrix?

A matrix that has no inverse

A matrix that is its own inverse

A matrix that has all identical rows

A matrix that has all identical columns

Question 43: What is Gaussian elimination used for?

Solving systems of linear equations by reducing a matrix to row echelon form

Solving systems of linear equations by multiplying matrices

Finding the determinant of a matrix

Finding the inverse of a matrix

Question 44: What is the pigeonhole principle used for in combinatorics?

Proving that if more items than containers are available, at least one container must contain more than one item

Proving that if fewer items than containers are available, each container holds one item

Proving that every possible combination of items fits into the containers

Proving that there are more containers than items

Question 45: Which of the following best describes a path in graph theory?

A sequence of vertices connected by edges, with no repeated vertices

A sequence of vertices connected by edges, where vertices and edges can be repeated

A sequence of vertices where all vertices are adjacent

A sequence of edges where all edges are adjacent

Question 46: Which of the following describes a non-connected graph?

A graph where there is at least one vertex that cannot be reached from any other vertex

A graph where all vertices are reachable from any other vertex

A graph that has only one vertex

A graph that has more edges than vertices

Question 47: What is the primary use of a depth-first search (DFS) algorithm in graph theory?

To explore a graph by visiting all vertices and edges in a linear order

To find the shortest path between two vertices

To explore as far as possible along each branch before backtracking

To find all cycles in a graph

Question 48: Which of the following is true for a breadth-first search (BFS) algorithm?

It explores the graph layer by layer, visiting all neighbors at the present depth before moving on

It only explores the graph along a single path until it reaches a dead end

It finds the longest path in a graph

It is not suitable for finding the shortest path between two vertices

Question 49: In the context of graph theory, what is a clique?

A subset of vertices such that every two distinct vertices are adjacent

A subset of vertices with no edges connecting them

A path that visits every vertex exactly once

A vertex that connects to all other vertices

Question 50: Which of the following statements about trees is true?

A tree is a connected graph with no cycles

A tree is a disconnected graph with cycles

A tree can have more than one root

A tree must have at least two vertices

Congratulations! You have completed all 5 question sets. Good job!

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