Question

Construct a 3 × 4 matrix A = [a_ij] whose elements a_ij are given by:

`a_(ij)=1/2= -3i + j `

Answer 1

`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]]`