A simple Linear Algebra question that seems so hard

In summary, the statement discusses whether the determinant of a matrix remains unchanged when the columns are written in reverse order. One method of finding the determinant is through cofactor expansion. By switching the columns, the sign of the cofactors would change but the overall value of the determinant would remain the same.
  • #1
qwerty11
39
0

Homework Statement



Is the statement true or sometimes false. Justify your answer:

The determinant of a matrix is unchanged if the columns are written in reverse order.

Homework Equations





The Attempt at a Solution



I understand that the only thing that is changed is the sign (negative to positive or visa-versa), but do not understand the proof of how.
 
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  • #2
how do you find the determinant of a matrix?
 
  • #3
One way would be via cofactor expansion.

I.e. 3x3 matrix determinant =a11C11+a12C12+a13C13
 
  • #4
okay good. so if you switched the columns, how would the cofactor expansion change?
 
  • #5
and calculate out those cofactors when you do it.
 

Related to A simple Linear Algebra question that seems so hard

1. What is Linear Algebra?

Linear Algebra is a branch of mathematics that deals with linear equations and their representations in vector spaces. It involves the study of linear systems of equations, matrices, and vector spaces.

2. What makes a Linear Algebra question seem difficult?

A Linear Algebra question may seem difficult due to its complex notation, use of abstract concepts, or because it requires a deep understanding of the underlying principles and techniques. Additionally, some Linear Algebra problems may involve multiple steps and require a strong grasp of algebraic manipulations.

3. How can I improve my understanding of Linear Algebra?

The best way to improve your understanding of Linear Algebra is through practice. Solving a variety of problems can help you become familiar with different types of questions and develop your problem-solving skills. Additionally, studying the underlying concepts and principles can also help deepen your understanding.

4. What are some real-world applications of Linear Algebra?

Linear Algebra has many real-world applications, including computer graphics, data analysis, machine learning, and engineering. It is also used in physics, economics, and statistics, among other fields.

5. How can I approach a seemingly difficult Linear Algebra question?

When faced with a difficult Linear Algebra question, it is important to break it down into smaller, more manageable parts. Start by identifying the given information and what is being asked for. Then, try to apply the relevant concepts and techniques to solve each part of the question. It can also be helpful to seek assistance from a tutor or study group if needed.

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