# Linear Algebra when to write matrix as a col. vector vs a row vector

• bchapa26
In summary, when finding the kernel, the given vectors should be written as columns of a matrix. However, for other cases such as linear transformations and basis, there may not be a specific rule and it is important to understand the concept rather than memorizing.
bchapa26
1. My question is a general question that I need the answer to so that I can fully understand the homework I am doing. When do I write given vectors as columns of a matrix, and when do I write them as rows of a matrix? More specifically, how do I write the vectors when finding:

1) Ker(T)
2) Linear Transformations
3) Basis

And rather than memorizing, is there a way to logically understand why I am writing the vectors as such? I'm sorry if this is vague, I am just trying to understand this material better. Thank you!

For finding the kernel you make the vectors into columns. Not sure about the others.

## What is a matrix?

A matrix is a rectangular array of numbers or variables arranged in rows and columns. It is used to represent and manipulate data in many areas of mathematics and science.

## When should a matrix be written as a column vector?

A matrix should be written as a column vector when the data it represents is a list of values arranged vertically, such as a list of measurements or observations over time.

## When should a matrix be written as a row vector?

A matrix should be written as a row vector when the data it represents is a list of values arranged horizontally, such as a list of characteristics or features for a set of objects.

## How do you determine the dimensionality of a matrix?

The dimensionality of a matrix is determined by the number of rows and columns it contains. For example, a matrix with 3 rows and 4 columns has a dimensionality of 3 by 4 (or 3x4).

## Can a matrix be written both as a column vector and a row vector?

Yes, a matrix can be written as both a column vector and a row vector. This is useful for representing data in different ways and for performing different mathematical operations.

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