Question

Construct a 3 x 3 matrix, whose element aij are given by aij = { i-j ; if i >= j
i+j ; if i< j ​

Answer 1

Dear student
$$\begin{gathered} \mathrm{let}\mathrm{the}\mathrm{matrix}\mathrm{be} \\ \left[\begin{array}{ccc}{\mathrm{a}}_{11}& {\mathrm{a}}_{12}& {\mathrm{a}}_{13}\\ {\mathrm{a}}_{21}& {\mathrm{a}}_{22}& {\mathrm{a}}_{23}\\ {\mathrm{a}}_{31}& {\mathrm{a}}_{32}& {\mathrm{a}}_{33}\end{array}\right] \\ {\mathrm{a}}_{11}=1-1=0 \\ {\mathrm{a}}_{12}=1+2=3 \\ {\mathrm{a}}_{13}=1+3=4 \\ {\mathrm{a}}_{21}=2-1=1 \\ {\mathrm{a}}_{22}=2-2=0 \\ {\mathrm{a}}_{23}=2+3=5 \\ {\mathrm{a}}_{31}=3-1=2 \\ {\mathrm{a}}_{32}=3-2=1 \\ {\mathrm{a}}_{33}=3-3=0 \\ \mathrm{so}\mathrm{the}\mathrm{matrix}\mathrm{is} \\ \left[\begin{array}{ccc}0& 3& 4\\ 1& 0& 5\\ 2& 1& 0\end{array}\right] \end{gathered}$$
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