2.1 Matrices - SPM Mathematics

2.1 Matrices

A matrix is a rectangular array of numbers enclosed in large brackets.

For example (\begin{matrix} 2 & 0 \\ 3 & 1 \end{matrix}) is a matrix .

$For example (\begin{matrix} 2 & 0 \\ 3 & 1 \end{matrix}) is a matrix .$

(A) Rows, Columns and Order of Matrices

1. A matrix which has m rows and n columns is known as a matrix of order m × n.

2. A row matrix is a matrix which has only one row.

Example:

\begin{array}{l} (4), (2 6), (3 8    5) \\ 1 \times 1 1 \times 2 1 \times 3 \\ Only 1 row \end{array}

$\begin{array}{l} (4), (2 6), (3 8 5) \\ 1 \times 1 1 \times 2 1 \times 3 \\ Only 1 row \end{array}$

3. A column matrix is a matrix which has only one column.

Example:

\begin{array}{l} (3), (\begin{array}{l} 2 \\ 6 \end{array}), (\begin{array}{l} - 5 \\ 7 \\ - 9 \end{array}) \\ 1 \times 12 \times 13 \times 1 \\ Only 1 column \end{array}

$\begin{array}{l} (3), (\begin{array}{l} 2 \\ 6 \end{array}), (\begin{array}{l} - 5 \\ 7 \\ - 9 \end{array}) \\ 1 \times 12 \times 13 \times 1 \\ Only 1 column \end{array}$
4. A square matrix is a matrix which has equal number of rows and columns.
Example:

\begin{array}{l} (3), (\begin{matrix} 7 & 0 \\ 2 & 5 \end{matrix}), (\begin{matrix} 1 & 39 \\ \begin{array}{l} 0 \\ 6 \end{array} & \begin{array}{l} 41 \\ 35 \end{array} \end{matrix}) \\ 1 \times 12 \times 23 \times 3 \\ Number of rows = Number of columns \end{array}

$\begin{array}{l} (3), (\begin{matrix} 7 & 0 \\ 2 & 5 \end{matrix}), (\begin{matrix} 1 & 39 \\ \begin{array}{l} 0 \\ 6 \end{array} & \begin{array}{l} 41 \\ 35 \end{array} \end{matrix}) \\ 1 \times 12 \times 23 \times 3 \\ Number of rows = Number of columns \end{array}$

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