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प्रश्न
Construct a 3 × 4 matrix, whose elements are given by `a_(ij) = 2i - 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) = 2i - j, i = 1,2,3 and j = 1,2,3,4`
`:. a_(11) = 2 xx 1 - 1 = 2 - 1 = 1`
`a_21 = 2xx2 - 1 = 4 -1 = 3`
`a_31 = 2xx3 -1 = 6 -1 = 5`
⇒ `a_12 = 2xx1-2 = 2-2 = 0`
`a_22 = 2xx2 - 2= 4 - 2 = 2`
`a_32 = 2 xx 3 - 2 = 6 - 2 = 4`
⇒ `a_13 = 2xx1-3= 2-3 = -1`
`a_23 = 2xx2-3= 4-3 = 1`
`a_33 = 2xx3 -3 = 6 - 3 = 3`
⇒ `a_14 = 2xx1 - 4= 2 - 4 = -2`
`a_24 = 2xx2 -4 = 4 - 4 = 0`
`a_34 = 2xx3-4 = 6 - 4 = 2`
Therefore, the required matrix is `A = [(1,0,-1,-2),(3,2,1,0),(5,4,3,2)]`
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