Question

Construct a 3 × 4 matrix, whose elements are given by:

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

Answer 1

In general, a 3 × 4 matrix is given by A = `[(a_11, a_12,a_13,a_14), (a_21,a_22, a_23, a_24), (a_31,a_32, a_33, a_34)]`

`a_(ij) = 1/2 |-3i + j|`, i = 1, 2, 3 and j = 1, 2, 3, 4

`a_11 = 1/2 |-3xx1+1|`

= `1/2|-3+1|`

= `1/2|-2|`

= `2/2`

= 1

`a_12 = 1/2|-3xx1+2|`

= `1/2|-3+2|`

= `1/2|-1|`

= `1/2`

`a_13 = 1/2|-3xx1+3|`

= `1/2|-3+3|`

= 0

`a_14 = 1/2 |-3xx1+4|`

= `1/2|-3+4|`

= `1/2|1|`

= `1/2`

`a_21 = 1/2|-3xx2+1|`

= `1/2|-6+1|`

= `1/2|-5|`

= `5/2`

`a_22 = 1/2|-3xx2+2|`

= `1/2|-6+2|`

= `1/2|-4|`

= `4/2`

= 2

`a_23 = 1/2|-3xx2+3|`

= `1/2|-6+3|`

= `1/2|-3|`

= `3/2`

`a_24 = 1/2|-3xx2+4|`

= `1/2 |-6+4`

= `1/2|-2|`

= `2/2`

= 1

`a_31 = 1/2|-3xx3+1|`

= `1/2|-9+1|`

= `1/2|-8|`

= `8/2`

= 4

`a_32 = 1/2|-3xx3+2|`

= `1/2|-9+2|`

= `1/2|-7|`

= `7/2`

`a_33 = 1/2 |-3xx3+3|`

= `1/2|-9+3|`

= `1/2|-6|`

= `6/2`

= 3

`a_34 =  1/2 |-3xx3+4|`

= `1/2 |-9+4|`

= `1/2|-5|`

= `5/2`

Therefore, the required matrix is A = `[(1, 1/2, 0, 1/2), (5/2, 2, 3/2, 1), (4, 7/2, 3,5/2)]`