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# In the matrix $A=\begin{bmatrix}2 & 5 & 19 & -7\\35 & -2 & \frac{5}{2} & 12\\\sqrt 3 & 1 & -5& 17\end{bmatrix},$write:$(i)\;The\;order\;of\;the\;matrix,\qquad(ii)\;The\;number\;of\;the\;elements,$$(iii)\;Write\;the\;elements\;a_{13},a_{21},a_{33},a_{24},a_{23}$

Toolbox:
• Order of matrix=A matrix having m rows and n column is called matrix of order $m\times n$ or simply $m\times n.$
• Number of elements in a matrix=Product of rows and columns in a matrix.
• i.e $m\times n.$
• m=rows,n=column.
• Elements of matrix:$a_ij$
• It is element lying in the $i^{th}$ row and $j^{th}$ column.
In the given matrix we have 3 rows and 4 column.

Order of matrix is $3\times 4.$

Element of matrix=row $\times$ column.

In the above matrix we have 3 rows and 4 columns

Number of elements=$3\times 4$

$\qquad\qquad\qquad\;\;\;=12.$

The element $a_{13}$

$a_{13}\rightarrow$ $1^{st}$ row and $3^{rd}$ column $a_{13}=19.$

$a_{21}\rightarrow$ $2^{nd}$ row and $1^{st}$ column $a_{21}=35.$

$a_{33}\rightarrow$ $3^{rd}$ row and $3^{rd}$ column $a_{33}=-5.$

$a_{24}\rightarrow$ $2^{nd}$ row and $4^{th}$ column $a_{24}=12.$

$a_{23}\rightarrow$ $2^{nd}$ row and $3^{rd}$ column $a_{23}=\frac{5}{2}.$