A matrix (pronounced MAYtrix) is a rectangular arrangement of numbers, like:
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$$
\begin{bmatrix}
7 & 3 & 2\\
6 & 5 & 8
\end{bmatrix}
$$
A number in a matrix is often called an element, a member, or an entry of the matrix.
The members of a matrix are often enclosed in (square) brackets.
Rows have a horizontal orientation, and are numbered from top to bottom:
$7$  $3$  $2$ 
$6$  $5$  $8$ 
Columns have a vertical orientation, and are numbered from left to right:
$7$  $3$  $2$  
$6$  $5$  $8$ 
The plural of matrix is matrices (pronounced MAYtrisees).
Matrices offer a way to represent large amounts of data in an organized way.
Matrices are particularly wellsuited to computer analysis.
There are a multitude of applications of matrices, including:
The size of a matrix is reported by stating the number of rows, followed by the ‘$\,\times\,$’ symbol, followed by the number of columns.
For example, the size of
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$
\begin{bmatrix}
7 & 3 & 2\\
6 & 5 & 8
\end{bmatrix}
$
is $\,2\times 3\,$,
which is read aloud as ‘$\,2\,$ by $\,3\,$’.
Observe that an $\,m \times n\,$ matrix has $\,mn\,$ elements,
since there are $\,m\,$ rows, with $\,n\,$ entries in each row.
Matrices are usually named with capital letters.
Members of a matrix are usually named with lowercase letters.
In particular, the elements of a matrix $\,M\,$ are conventionally named
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$\,m_{ij}\,$:
For example, if
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$
M =
\begin{bmatrix}
7 & 3 & 2\\
6 & 5 & 8\end{bmatrix}
$
then:
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$\,m_{11} = 7\,$ (first row, first column; read as em sub one one, NOT (say) em sub eleven)
$\,m_{12} = 3\,$ (first row, second column)
$\,m_{13} = 2\,$ (first row, third column)
$\,m_{21} = 6\,$ (second row, first column)
$\,m_{22} = 5\,$ (second row, second column)
$\,m_{23} = 8\,$ (second row, third column)
$A=B$  if and only if 
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$A\,$ and $\,B\,$ have the same size and $\,a_{ij} = b_{ij}\,$ for all $\,i\,$ and $\,j\,$. 
A matrix with the same number of rows and columns is called a square matrix.
For example,
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$
\begin{bmatrix}
1 & 2\\
3 & 4
\end{bmatrix}
$ is a square matrix.
A matrix where all the entries are zero is called a zero matrix.
For example,
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$
\begin{bmatrix}
0 & 0 & 0 & 0\\
0 & 0 & 0 & 0
\end{bmatrix}
$ is a $\,2\times 4\,$ zero matrix.
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
