Matrices

 2.1 Matrices

 Definition of a matrix A matrix is a set of numbers arranged in rows and columns to form a rectangular or a square array.

 What is order of a matrix? Order of a matrix can be determined by counting the number of rows followed by the number of columns of the matrix. Matrix with $$m$$ rows and $$n$$ columns has the order $$m\times n$$ and is read as “matrix $$m$$ by $$n$$”. For example, For example: \begin{aligned}\begin{bmatrix} 2&3&7\\ 5&4&9 \end{bmatrix}\end{aligned} This matrix has $$2$$ rows and $$3$$ columns. Therefore, it is a matrix with order $$2\times 3$$ and can be read as “matrix $$2$$ by $$3$$”.

 Example 1 Given that matrix K=\begin{aligned}\begin{bmatrix} -2&3\\ 0&4\\1&9\end{bmatrix}\end{aligned}, determine a) the order of the matrix, b) the elements $$d_{11}$$, $$d_{21}$$ and $$d_{32}$$. Solution: a)Since D has $$3$$ rows and $$2$$ columns, $$\therefore$$ D has order $$3\times 2$$ \begin{aligned} b)\hspace{1mm} &d_{11}=-2\end{aligned} $$\because$$ $$d_{11}$$ is the element at the first row and first column. \begin{aligned}d_{21}=0\end{aligned} $$\because$$ $$d_{21}$$  is the element at the second row and first column. \begin{aligned} d_{32}=9\end{aligned} $$\because$$ $$d_{32}$$ is the element at the third row and second column.

 Equal matrices Matrixces A and B are equal, A = B if the order of both the matrices are the same and the corresponding elements are equal. \begin{aligned} \begin{bmatrix} a&b\\ c&d \end{bmatrix} = \begin{bmatrix} e&f\\ g&h \end{bmatrix} \end{aligned} \begin{aligned} \implies a&=e, \\b&=f,\\c&=g,\\d&=h \end{aligned}