Question

Construct a 2×2 matrix, A = [aij] whose element is aij = i/j​

Answer 1

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Answer 2

Solution -

We know that, elements for 2×2 matrix are :-

• $\sf{a_{11}}$
• $\sf{a_{12}}$
• $\sf{a_{21}}$
• $\sf{a_{22}}$

⠀

★ $\bf{For\: a_{11},\: i = 1\: and\: j = 1}$

$\tt\dashrightarrow{a_{11} = \dfrac{1}{1} = 1}$

⠀

★ $\bf{For\: a_{12},\: i = 1\: and\: j = 2}$

$\tt\dashrightarrow{a_{12} = \dfrac{1}{2}}$

⠀

★ $\bf{For\: a_{21},\: i = 2\: and\: j = 1}$

$\tt\dashrightarrow{a_{21} = \dfrac{2}{1} = 2}$

⠀

★ $\bf{For\: a_{22},\: i = 2\: and\: j = 2}$

$\tt\dashrightarrow{a_{22} = \dfrac{2}{2} = 1}$

⠀

Now, we have all the elements of matrix.

Therefore, the required matrix is

⠀⠀⠀⠀⠀$\tt\longrightarrow{}$ $\left[ \begin{array}{cc}1& \frac{1}{2} \\ 2 & 1\end{array} \right]$