Question

construct 3× 2 matrix whose elements are gives by aij= 1/2 |i- 3j|?​

Answer 1

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

Let us assume a matrix of order 3 × 2 as

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

Now, it is given that

$\red{\bf :\longmapsto\:a_{ij} = \dfrac{1}{2} |i - 3j| \: \: }$

So,

$\red{\bf :\longmapsto\:a_{11} = \dfrac{1}{2} |1 - 3| = \dfrac{1}{2} | - 2| = 1 \: \: }$

$\red{\bf :\longmapsto\:a_{12} = \dfrac{1}{2} |1 - 6| = \dfrac{1}{2} | - 5| = \dfrac{5}{2} \: \: }$

$\red{\bf :\longmapsto\:a_{21} = \dfrac{1}{2} |2 - 3| = \dfrac{1}{2} | - 1| = \dfrac{1}{2} \: \: }$

$\red{\bf :\longmapsto\:a_{22} = \dfrac{1}{2} |2 - 6| = \dfrac{1}{2} | - 4| = 2\: \: }$

$\red{\bf :\longmapsto\:a_{31} = \dfrac{1}{2} |3 - 3| = \dfrac{1}{2} |0| = 0 \: \: }$

$\red{\bf :\longmapsto\:a_{32} = \dfrac{1}{2} |3 - 6| = \dfrac{1}{2} | - 3| = \dfrac{3}{2} \: \: }$

So, on substituting the values, we get

$\rm :\longmapsto\:A = \begin{gathered}\sf \:\left[\begin{array}{cc}1&\dfrac{5}{2} \\ \\\dfrac{1}{2} &2 \\ \\ 0&\dfrac{3}{2} \end{array}\right]\end{gathered}$

Additional Information :-

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

2. Order give the following information :

(a). Number of elements in given matrix.

(b). Number of elements in each row

(c). Number of elements in each column