Possibilities of the Number of Solutions of a Homogeneous System of Linear Equations
Problem 14
Here is a very short true or false problem.
Select either True or False. Then click “Finish quiz” button.
You will be able to see an explanation of the solution by clicking “View questions” button.
Sponsored Links
System of linear equations
Quizsummary
0 of 1 questions completed
Questions:
 1
Information
Determine whether the following sentence is True or False.
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Results
0 of 1 questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 points, (0)
Average score 

Your score 

Categories
 Not categorized 0%
 1
 Answered
 Review

Question 1 of 1
1. Question
If a homogeneous system of linear equations has a nontrivial solution, then the system has infinitely many solutions.
Correct
Way to go! The possibility of the number of solutions of any system of linear equations are zero, one, or infinity.
Since a homogeneous system has the zero solution, if it has nontrivial solutions, it has two solutions. Hence there should be infinitely many solutions.Incorrect
Review the following fact: the possibility of the number of solutions of any system of linear equations are zero, one, or infinity.
Since a homogeneous system has the zero solution, if it has nontrivial solutions, it has two solutions. Hence there should be infinitely many solutions.
Add to solve later
Sponsored Links
More from my site
 Summary: Possibilities for the Solution Set of a System of Linear Equations In this post, we summarize theorems about the possibilities for the solution set of a system of linear equations and solve the following problems. Determine all possibilities for the solution set of the system of linear equations described below. (a) A homogeneous system of $3$ […]
 True or False: $(AB)(A+B)=A^2B^2$ for Matrices $A$ and $B$ Let $A$ and $B$ be $2\times 2$ matrices. Prove or find a counterexample for the statement that $(AB)(A+B)=A^2B^2$. Hint. In general, matrix multiplication is not commutative: $AB$ and $BA$ might be different. Solution. Let us calculate $(AB)(A+B)$ as […]
 Quiz: Possibilities For the Solution Set of a Homogeneous System of Linear Equations 4 multiple choice questions about possibilities for the solution set of a homogeneous system of linear equations. The solutions will be given after completing all problems. (The Ohio State University, Linear Algebra Exam)
 10 True of False Problems about Nonsingular / Invertible Matrices 10 questions about nonsingular matrices, invertible matrices, and linearly independent vectors. The quiz is designed to test your understanding of the basic properties of these topics. You can take the quiz as many times as you like. The solutions will be given after […]
 Quiz 1. GaussJordan Elimination / Homogeneous System. Math 2568 Spring 2017. (a) Solve the following system by transforming the augmented matrix to reduced echelon form (GaussJordan elimination). Indicate the elementary row operations you performed. […]
 True or False Quiz About a System of Linear Equations (Purdue University Linear Algebra Exam) Which of the following statements are true? (a) A linear system of four equations in three unknowns is always inconsistent. (b) A linear system with fewer equations than unknowns must have infinitely many solutions. (c) […]
 True or False. Every Diagonalizable Matrix is Invertible Is every diagonalizable matrix invertible? Solution. The answer is No. Counterexample We give a counterexample. Consider the $2\times 2$ zero matrix. The zero matrix is a diagonal matrix, and thus it is diagonalizable. However, the zero matrix is not […]
 Quiz: Linear Equations and Matrix Entreis Do the following quiz about Linear Equations Matrix entries. There are two questions. After completing the quiz, click View questions to see the solutions.