Question

construct a 3×2 matria whose elements are given by aij=|i-2j|÷2​

Answer 1

$\large\underline{\sf{Solution-}}$

Let us assume a matrix of 3 × 2 order as

$</p><p>\begin{gathered}\rm :\longmapsto\:A = \begin{gathered}\sf \:\left[\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\\a_{31}&a_{32}\end{array}\right]\end{gathered}\end{gathered}$

It is given that

$\red{\sf :\longmapsto\:a_{ij} = \dfrac{1}{2} |i - 2j| }$

Now,

$\red{\sf :\longmapsto\:a_{11} = \dfrac{1}{2} |1 - 2| = \dfrac{1}{2} | - 1| = \dfrac{1}{2} }$

$\red{\sf :\longmapsto\:a_{12} = \dfrac{1}{2} |1 - 4| = \dfrac{1}{2} | - 3| = \dfrac{3}{2} }$

$\red{\sf :\longmapsto\:a_{21} = \dfrac{1}{2} |2 - 2| = \dfrac{1}{2} |0| = 0}$

$\red{\sf :\longmapsto\:a_{22} = \dfrac{1}{2} |2 - 4| = \dfrac{1}{2} | - 2| = 1}$

$\red{\sf :\longmapsto\:a_{31} = \dfrac{1}{2} |3 - 2| = \dfrac{1}{2} |1| = \dfrac{1}{2} }$

$\red{\sf :\longmapsto\:a_{32} = \dfrac{1}{2} |3 - 4| = \dfrac{1}{2} | - 1| = \dfrac{1}{2} }$

Thus,

$</p><p> \purple{\begin{gathered}\rm :\longmapsto\:A = \begin{gathered}\sf \:\left[\begin{array}{cc}\dfrac{1}{2} &\dfrac{3}{2} \\ \\ 0&1 \\ \\\dfrac{1}{2} &\dfrac{1}{2} \end{array}\right]\end{gathered}\end{gathered}}$

More to know :-

1. Order of a matrix is defined as number of rows × number of columns.

2. Order of a matrix provides the following information :-

(a). Number of elements in a matrix.

(b). Number of elements in each row.

(c). Number of elements in each column.