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प्रश्न
Construct a 3 × 4 matrix, whose elements are given by `a_(ij) = 1/2 |-3i + j|`
उत्तर
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)]`
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