Question

Construct a 3 X 2 matrix whose elements are given by $straight a subscript ij equals 1 half left square bracket straight i minus 3 space straight j right square bracket$

Solution

Let A = [a_{i j} ) be required 3x2 matrix, where

straight a subscript ij equals 1 half left square bracket straight i minus 3 space straight j right square bracket

straight a subscript 11 equals 1 half open vertical bar 1 minus 3 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 1 minus 6 close vertical bar equals 1 half left parenthesis 5 right parenthesis equals 5 over 2 straight a subscript 21 equals 1 half open vertical bar 2 minus 3 close vertical bar equals 1 half left parenthesis 1 right parenthesis equals 1 half. space straight a subscript 22 equals 1 half open vertical bar 2 minus 6 close vertical bar equals 1 half left parenthesis 4 right parenthesis equals 2 straight a subscript 31 equals 1 half open vertical bar 3 minus 3 close vertical bar equals 1 half left parenthesis 0 right parenthesis equals 0 comma space space space space straight a subscript 32 equals 1 half open vertical bar 3 minus 6 close vertical bar equals 1 half left parenthesis 3 right parenthesis equals 3 over 2 straight A equals open square brackets table row 1 cell 5 over 2 end cell row cell 1 half end cell 2 row 0 cell 3 over 2 end cell end table close square brackets

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