Understanding 3x3 Matrices: An Overview

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A 3x3 matrix is a grid of numbers arranged in three rows and three columns, which can represent linear transformations in three-dimensional space. The null vector, represented as (0, 0, 0), serves as the identity element for vector addition, meaning any vector added to the null vector remains unchanged. To find a null vector for a 2x2 matrix, one must identify a non-null vector that, when multiplied by the matrix, results in the null vector. The discussion emphasizes the distinction between null vectors and matrices while seeking clarity on how to apply these concepts in practical examples. Understanding these foundational elements is crucial for working with matrices and vector spaces effectively.
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I have no idea what this is! Please can someone explain comparing to a 3x3 matrix?
 
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The null vector is the neutral element of addition in a vectorspace: ##\vec{a}+\vec{0}=\vec{a}##.

In our 3-dimensional space, for example, it can be written as

$$\begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}$$

I don't see a reasonable way to compare it to a 3x3-matrix.
 
mfb said:
The null vector is the neutral element of addition in a vectorspace: ##\vec{a}+\vec{0}=\vec{a}##.

I have a question in my notes saying 'Find a null vector for the following matricies'. They are all 2x2. Can you give an example showing how to do it?
 
Post the full problem statement, please.

I would guess that you should find a (not null) vector, which, multiplied with your matrices, gives the null vector as result.
 

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