1. Tardigrade
  2. Question
  3. Mathematics
  4. if A = [aij]4×3 where aij=(i-j/i+j),then find A

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. if $A = \left[a_{ij}\right]_{_{4\times3}}$ where $a_{ij}=\frac{i-j}{i+j}$,then find $A$

Matrices

Solution:

Here, $a_{ij}=\frac{i-j}{i+j}$
$a_{11}=\frac{1-1}{1+1}=0$,
$a_{12}=\frac{1-2}{1+2}=\frac{-1}{3}$,
$a_{13}=\frac{1-3}{1+3}=\frac{-1}{2}$,
$a_{21}=\frac{2-1}{2+1}=\frac{1}{3}$,
$a_{22}=\frac{2-2}{2+2}=0$,
$a_{23}=\frac{2-3}{2+3}=\frac{-1}{5},$
$a_{31}=\frac{3-1}{3+1}=\frac{1}{2}$,
$a_{32}=\frac{3-2}{3+2}=\frac{1}{5}$,
$a_{33}=\frac{3-3}{3+3}=0,$
$a_{41}=\frac{4-1}{4+1}=\frac{3}{5}$,
$a_{42}=\frac{4-2}{4+2}=\frac{1}{3}$,
$a_{43}=\frac{4-3}{4+3}=\frac{1}{7}$
so, required matrix is$\begin{bmatrix}0&-\frac{1}{3}&-\frac{1}{2}\\ \frac{1}{3}&0&-\frac{1}{5}\\ \frac{1}{2}&\frac{1}{5}&0\\ \frac{3}{5}&\frac{1}{3}&\frac{1}{7}\end{bmatrix}$