Show that this column matrix is not a vector

In summary, the conversation discusses the transformation of a columns matrix and whether it can be considered as a vector. One person suggests using a rotation matrix with Euler angles, but another person argues that this may not be the most efficient approach. The idea of simplifying the problem to a rotation about the z-axis is brought up, and it is suggested to focus on the z component and how it is affected by the rotation. The moderator then notes that this conversation is moved to the homework forum and requests for an attempt at a solution from one of the participants.
  • #1
Summary:: I am suppose to show that this columns matrix does not transform as a vector. In another words, it is not in fact a vector.


I think this become trivial if we get the rotation matrix composed of Euler angles. But, i think that it is not the best way to solve this problem, and i can't find another way.
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  • #2
This is not my area of expertise, but I think you can simplify it to a rotation about the z-axis. That matrix is much simpler. I think you might only need to look at the z component, and show that you get a different result when the rotation is applied to the 3rd term in that array.
  • #3
Moderator's note: Thread moved to homework forum.

@Herculi, please give an attempt at a solution.

1. What is a column matrix?

A column matrix is a rectangular array of numbers arranged in a single column. It is used to represent a set of data or values in a concise and organized manner.

2. How is a column matrix different from a vector?

A vector is a mathematical object that has both magnitude and direction, while a column matrix is simply a way of organizing data. Vectors can be represented as column matrices, but not all column matrices are considered vectors.

3. What are the characteristics of a vector?

Vectors have magnitude, direction, and can be added, subtracted, and multiplied by a scalar. They also follow the rules of vector algebra, such as the commutative and associative properties.

4. How can I tell if a column matrix is not a vector?

A column matrix is not a vector if it does not have a direction or if it does not follow the rules of vector algebra. Additionally, a column matrix with only one column is not considered a vector since it does not have both magnitude and direction.

5. Why is it important to distinguish between column matrices and vectors?

It is important to distinguish between column matrices and vectors because they have different properties and uses in mathematics and science. Vectors are often used to represent physical quantities such as force and velocity, while column matrices are used for organizing and analyzing data sets. Knowing the difference can help avoid confusion and ensure accurate calculations and interpretations.

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