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Question

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

$straight a subscript ij equals 1 half open vertical bar negative 3 straight i plus straight j close vertical bar$

Solution

Let A = [a_{i j} be required 3x4 matrix where

straight a subscript ij equals 1 half open vertical bar negative 3 straight i plus straight j close vertical bar

therefore space space straight a subscript 11 equals 1 half open vertical bar negative 3 plus 1 close vertical bar equals 1 half left parenthesis 2 right parenthesis equals 1 comma space space space straight a subscript 12 equals 1 half open vertical bar negative 3 plus 2 close vertical bar equals 1 half left parenthesis 1 right parenthesis equals 1 half space space space space space straight a subscript 13 equals 1 half open vertical bar negative 3 plus 3 close vertical bar equals 1 half left parenthesis 0 right parenthesis equals 0 comma space space space straight a subscript 14 equals 1 half open vertical bar negative 3 plus 4 close vertical bar equals 1 half left parenthesis 1 right parenthesis equals 1 half space space space space space straight a subscript 21 equals 1 half open vertical bar negative 6 plus 1 close vertical bar equals 1 half left parenthesis 5 right parenthesis equals 5 over 2 comma space space space straight a subscript 22 equals 1 half open vertical bar negative 6 plus 2 close vertical bar equals 1 half left parenthesis 4 right parenthesis equals 2 space space space space space straight a subscript 23 equals 1 half open vertical bar negative 6 plus 3 close vertical bar equals 1 half left parenthesis 3 right parenthesis equals 3 over 2 comma space space space straight a subscript 24 equals 1 half open vertical bar negative 6 plus 4 close vertical bar equals 1 half left parenthesis 3 right parenthesis equals 1 space space space space space straight a subscript 31 equals 1 half open vertical bar negative 9 plus 1 close vertical bar equals 1 half left parenthesis 8 right parenthesis equals 4 comma space space space straight a subscript 32 equals 1 half open vertical bar negative 9 plus 2 close vertical bar equals 1 half left parenthesis 7 right parenthesis equals 7 over 2 space space space space space straight a subscript 33 equals 1 half open vertical bar negative 9 plus 3 close vertical bar equals 1 half left parenthesis 6 right parenthesis equals 3 comma space space space straight a subscript 34 equals 1 half open vertical bar negative 9 plus 4 close vertical bar equals 1 half left parenthesis 5 right parenthesis equals 5 over 2 therefore space space space space space straight A equals open square brackets table row 1 cell 1 half end cell 0 cell 1 half end cell row cell 5 over 2 end cell 2 cell 3 over 2 end cell 1 row 4 cell 7 over 2 end cell 3 cell 5 over 2 end cell end table close square brackets

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