Proof a property for a 3x3 matrix

In summary, the discussion focused on a 3x3 matrix A that satisfies the condition that the vectors Av and v are orthogonal for any vector v in R3. The task at hand is to prove that the transposed matrix At added to A is equal to 0. The member was reminded to show their work and put in effort before seeking help on the forum. The member then questioned if matrix A is a zero matrix and stated that they were having difficulty understanding the concept. However, after being reminded of the forum's purpose, the thread was closed.
  • #1
mathodman
3
0
Homework Statement
Let a 3 × 3 matrix A be such that for any vector of a column v ∈ R3 the vectors Av and v are orthogonal. Prove that At + A = 0, where At is the transposed matrix.
Relevant Equations
A is a zero matrix?
Let a 3 × 3 matrix A be such that for any vector of a column v ∈ R3 the vectors Av and v are orthogonal. Prove that At + A = 0, where At is the transposed matrix.
 
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  • #2
Welcome to the PF. :smile:

At the PF, we need you to show your best efforts to work on the problem before we can offer any tutorial help. Please show your work, so we can guide your efforts. Thanks.
 
  • #3
Hi! i don't know maybe matrix A is like zero matrix. I guess its something easy but i just don't get it right now
 
  • #4
That's not enough work. Please show more, or your thread will be closed. Thank you.
 
  • #5
alright, i guess its not a forum for discussions, thanks anyway
 
  • #6
It's a forum that helps students to learn. And to learn how to learn. That's in the rules that you agreed to when you joined. If you've looking to cheat on your homework, this isn't the place for you. Thread is closed.
 
  • Like
Likes baldbrain, jim mcnamara and mathodman

FAQ: Proof a property for a 3x3 matrix

1. What is a 3x3 matrix?

A 3x3 matrix is a rectangular array of numbers or variables arranged in 3 rows and 3 columns. It is commonly used in linear algebra and represents a linear transformation in three-dimensional space.

2. What is a property of a 3x3 matrix?

A property of a 3x3 matrix is a characteristic or attribute that is true for all matrices of this size. Examples of properties include determinants, eigenvalues, and rank.

3. Why is it important to prove a property for a 3x3 matrix?

Proving a property for a 3x3 matrix is important because it helps us understand the behavior and properties of matrices in general. It also allows us to make predictions and solve problems involving 3x3 matrices with confidence.

4. How can a property of a 3x3 matrix be proven?

A property of a 3x3 matrix can be proven using mathematical proofs and techniques. This may involve manipulating the matrix using operations such as row reduction, finding patterns in the matrix, or using theorems and formulas specific to the property being proved.

5. What are some real-life applications of 3x3 matrices?

3x3 matrices have many real-life applications, including computer graphics, robotics, and engineering. They can be used to represent 3D transformations, solve systems of linear equations, and model physical systems. They are also used in data analysis and financial calculations.

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