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### Course: Precalculus > Unit 7

Lesson 1: Introduction to matrices# Intro to matrices

Matrix is an arrangement of numbers into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements.

A

**matrix**is a rectangular arrangement of numbers into rows and columns.For example, matrix $A$ has two

**rows**and three**columns**.## Matrix dimensions

The

**dimensions**of a matrix tells its size: the number of rows and columns of the matrix,*in that order*.Since matrix $A$ has ${\text{two rows}}$ and ${\text{three columns}}$ , we write its dimensions as ${2}\times {3}$ , pronounced "two by three".

In contrast, matrix $B$ has ${\text{three rows}}$ and ${\text{two columns}}$ , so it
is a ${3}\times {2}$ matrix.

When working with matrix dimensions, remember ${\text{rows}}\times {\text{columns}}$ !

### Check your understanding

## Matrix elements

A

**matrix element**is simply a matrix entry. Each element in a matrix is identified by naming the row and column in which it appears.For example, consider matrix $G$ :

The element ${g}_{{2},{1}}$ is the entry in the ${\text{second row}}$ and the ${\text{first column}}$ .

In this case ${g}_{2,1}={18}$ .

In general, the element in ${\text{row}i}$ and ${\text{column}j}$ of matrix $A$ is denoted as ${a}_{{i},{j}}$ .

### Check your understanding

## Want to join the conversation?

- On problem six why doesn't answer B not satisfy the equation? But answer C does? The six is in the same spot as in both answers.(0 votes)
- Because, first part of the question (Matrix 2 x 3) is not the condition second option satisfies.(119 votes)

- Hi my name is Sayan, I still haven't understood the relevance of matrices. My request to you would be if you could give a real life scenario where matrices are used and/or another place where it has a practical use in everyday life. Also do explain this with an example for my better understanding?(28 votes)
- Matrix manipulation are used in video game creation, computer graphics techniques, and to analyze statistics. There are many more uses for matrices, but they tend to show up in more deeper understandings of disciplines.(42 votes)

- on problem 6, why is the answer c and not b ? it is the same answer just in different positions.(6 votes)
- No, since it is row by columns, answer b would be a 3 x 2 matrix not a 2 x 3 matrix, hope this helps(30 votes)

- why is there two answers to question number 6?

the following are the answers:

1. (the one this page call correct) answer #3

2. (the one that is also correct but this page call wrong) answer #2(0 votes)- #2 is wrong because it is a 3x2 matrix. We always count rows first, then columns. How tall is the matrix (2) then how wide is it (3)? That leaves #3 and #4 as options. Row 1 column 2 = 6. That means #3 is the right choice.(37 votes)

- Can there be a matrix with 0x0. If yes, then how is it represented(6 votes)
- It could be just an empty matrix, like this: []

However, such a matrix could not contain any information and would therefore be useless.(11 votes)

- What are matrices used for in math?(5 votes)
- A lot of things can be thought of as transformations of space, taking every point in 3D space and moving it somewhere else. Matrices are a compact way of talking about and working with a certain class of transformations.(8 votes)

- This Is More Easier Than Vectors Why isn't This Taught Before Teaching Vectors(2 votes)
- You you have to learn about vectors first because you will be using matrices to apply transformations to vectors. This will also be linked to solving systems of equations and a whole bunch of other fun stuff :)(11 votes)

- Is [0] the same as an empty one []?(3 votes)
- Probably no, because [] is empty, but [0] isn't. They're called zero matrices and they're used in matrices the same way regular zeroes are.(7 votes)

- The i and j in matrices is inverse from the notation in Cartesian axes. Why is it defined so confusing?(6 votes)
- I hope this helps you to contain your confusion:

A matrix is like a list of vectors of the same space (same number of entries).

Let v be a vector such that v = {1, 2, 3}.

We write v as v =

| 1 |

| 2 |

| 3 |

Now let u be a new vector u =

| 4 |

| 5 |

| 6 |

A matrix can be thought of as a list of vectors, so a vector with vector entries (a matrix) could be A = {v, u}, written as A =

| 1 4 |

| 2 5 |

| 3 6 |

and that is a matrix. Notice that the columns are more closely related (of the same subvector), so it makes sense that we might want to consider vertical decent before horizontal comparison. This is oposite to the x and y (abscissa and ordinate) of the Cartesian axes.

Hope this helps!(2 votes)

- what is the purpose of such arrangement of numbers in a matrix?(3 votes)
- It essentially enables you to store data in such a way that you can easily perform operations on the entire data set.(5 votes)