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Question
Construct a 3 × 4 matrix A = [aij] whose elements aij are given by:
`a_(ij)=1/2= -3i + j `
Solution
`a_(ij)=1/2= -3i + j `
Here,
`a_(11)= 1/2 `|`-3(1)+1` |`=1/2|-2|=1 ,`
`a_12=1/2`|`-3(1)+2`| `=1/2 | -1 | = 1/2 ,
`a_13=1/2|-3(1)+3| =1/2 | 0 | =0, `
`a_14= 1/2 | -3 (1)+ 4 | = 1/2`
`a_21 = 1/2 | -3 (2) + 1 | = 1/2 | -5 | = 5/2 `
`a_22=1/2 | -3 (2)+2|= 1/2 |-4|=2 ,`
`a_23=1/2|-3(2)+ 3 | =1/2 , `
`a_24= 1/2 | -3 (2)+ 4| = 1/2 |-2 |= 1`
`a_31= 1/2 | -3(3)+ 1 | = 1/2 |-8| =4 ,`
`a_32 = 1/2 | -3 (3)+ 2 | = 1/2 |-7| = 7/2,`
`a_33 = 1/2 | - 3 (3)+ 3|=1/2|-6|=3 and `
`a_34 = 1/2 | -3 (3)+ 4 | = 1/2 |5|=5/2 `
So, the required matrix is `[[1 1/2 0 1/2],[5/2 2 3/2 1],[4 7/2 3 5/2]]`
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