M - Define a Matrix Lesson

Define a Matrix

A matrix is a way to arrange a set of numbers in rows and columns. The entries of a matrix are the numbers that are inside:

$\begin{bmatrix} -2 & 7 & 3\\ 5 & 6 & 1\\ -2 &-1 & 0\\ 3 & 3 & 4\\ \end{bmatrix}$

The matrix above has 4 rows and 3 columns, so we would say it is a 4x3 matrix.

Matrices that have the same number of rows and columns are called square matrices.

$\begin{bmatrix} 1 & -2 \\ 4 & 5 \\ \end{bmatrix}$

There are also special matrices called identity matrices, these matrices are square matrices that have 1's along the main diagonal and 0's everywhere else.

$\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix} \begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 &0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0& 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1\\ \end{bmatrix}$

At times, we want to refer to a specific entry in a matrix and we do that by referring to the location of the entry by using the row and column. For instance, here is a matrix:

$\begin{bmatrix} -1 & 4 & 7 \\ 3 & 0 & 2 \\ \end{bmatrix}$

We would call -1 entry $a_{1\:1}$ because it is in row 1, column 1.

We would call 4 entry $a_{1\:2}$ because it is in row 1, column 2.

We would call 3 entry $a_{2\:1}$ because it is in row 2, column 1.

We would call 2 entry $a_{2\:3}$ because it is in row 2, column 3.

We can use matrices to organize information. Let's try a problem:

The school store sells birthday hats, cards, and teddy bears. They buy their products at wholesale prices - the hats cost $2.50, the cards cost $0.90, and the teddy bears cost $3.10. They decorate these products and the decorations for the hats cost $1.50, the decorations for the cards cost $0.60, and the decorations for the teddy bears cost $1.70.

So, we can organize this data into a matrix:

Create a Matrix

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