Answer

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Hint: The number of rows and columns that a matrix has is called its dimension or its order. By convention rows are listed first and columns second. Numbers that appear in the rows and columns of the matrix are called elements of the matrix.

Complete step-by-step answer:

Given that:

$A = \left[ {\begin{array}{*{20}{c}}

2&5&{19}&{ - 7} \\

{35}&{ - 2}&{\dfrac{5}{2}}&{12} \\

{\sqrt 3 }&1&{ - 5}&{17}

\end{array}} \right]$

(i) In the given matrix

Number of rows is $3$

Number of columns is $4$

Therefore the order of the matrix is $3 \times 4$

(ii) Since the order of the given matrix is $3 \times 4$

So total number of elements in the matrix $ = 3 \times 4 = 12$

Hence the matrix has 12 elements.

(iii) The elements of any matrix is represented as ${a_{mn}}$ where $m$ represents row number and $n$ represents column number.

Here ${a_{13}}$ represents elements of the 1 st row and 3 rd column.

So, ${a_{13}} = 19$

Similarly

$

{a_{21}} = 35 \\

{a_{33}} = - 5 \\

{a_{24}} = 12 \\

{a_{23}} = \dfrac{5}{2} \\

$

Note: The given question has problems related to basic definition of matrix like order, element number etc. although these are very basic things but must not be ignored. In the given question the number of elements has been found out by multiplying the order of the matrix. It can also be found out by simple counting for lower order matrix, but for higher order matrix multiplication of the order is the best way.

Complete step-by-step answer:

Given that:

$A = \left[ {\begin{array}{*{20}{c}}

2&5&{19}&{ - 7} \\

{35}&{ - 2}&{\dfrac{5}{2}}&{12} \\

{\sqrt 3 }&1&{ - 5}&{17}

\end{array}} \right]$

(i) In the given matrix

Number of rows is $3$

Number of columns is $4$

Therefore the order of the matrix is $3 \times 4$

(ii) Since the order of the given matrix is $3 \times 4$

So total number of elements in the matrix $ = 3 \times 4 = 12$

Hence the matrix has 12 elements.

(iii) The elements of any matrix is represented as ${a_{mn}}$ where $m$ represents row number and $n$ represents column number.

Here ${a_{13}}$ represents elements of the 1 st row and 3 rd column.

So, ${a_{13}} = 19$

Similarly

$

{a_{21}} = 35 \\

{a_{33}} = - 5 \\

{a_{24}} = 12 \\

{a_{23}} = \dfrac{5}{2} \\

$

Note: The given question has problems related to basic definition of matrix like order, element number etc. although these are very basic things but must not be ignored. In the given question the number of elements has been found out by multiplying the order of the matrix. It can also be found out by simple counting for lower order matrix, but for higher order matrix multiplication of the order is the best way.

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