Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
Question
Construct a 2 $\times$ 2 matrix, A = [aij], whose element $a_{i j}=\frac{i}{j}$
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Answer
In general, a 2 $\times$ 2 matrix is given by A = $\left[\begin{array}{ll} {a_{11}} & {a_{12}} \\ {a_{21}} & {a_{22}} \end{array}\right]$ $a_{i j}=\frac{i}{j}; ~~~ i, j=1,2$ Therefore, $a_{11}=\frac{1}{1}=1$ $a_{12}=\frac{1}{2}$ $a_{21}=\frac{2}{1}=2$ $a_{22}=\frac{2}{2}=1$ Therefore, the required matrix is A = $\left[\begin{array}{ll} {1} & {\frac{1}{2}} \\ {2} & {1} \end{array}\right]$
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