Question

Construct a 4 × 3 matrix whose elements are

`a_(ij)= (i-j)/(i+j )`

Answer 1

`a_(ij)= (i-j)/(i+j )`

Here,

`a_11=(1-1)/(1+1)=0/2=0 ,`

`a_12=(1-2)/(1+2)=(-1) /3`

 

`a_13=(1-3)/(1+3)=(-2)/4=(-1)/2`

`a_21=(2-1)/(2+1)=1/3,`

`a_22=(2-2)/(2-2)=0/0=0` 

`a_23= (2-3)/(2+3)=(-1)/5`

`a_31 = (3-1)/(3+1)=2/4=1/2 ,`

`a_32=(3-2)/(3+2)=1/5`

`a_33=(3-3)/(3+3)=0/6=0`

`a_41=(4-1)/(4+1)=3/5 ,`

`a_42=(4-2)/(4+2)=2/6=1/3`

`a_43=(4-3)/(4+3)=1/7`

 

So, the required matrix is`[[     0     (-1)/3       (-1)/2],[ 1/3           0          ( -1)/5],[     1/2           1/5             0  ],[   3/5             1/3           1/7 ]]`