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Question
Construct a 4 × 3 matrix whose elements are
`a_(ij)= (i-j)/(i+j )`
Solution
`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 ]]`
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