Construct 2 - 2 matrix- A - a ij - whose elements are given by ii a ij - i - j

Here, A =[ a_11 amp; a_12; a_21 amp; a_22 ]_2 × 2, where a_ij=i/j. ∴ a_11=1/1=1,a_12 =1/2, a_21=2/1=2 and a_22=2/2=1 Hence, the required matrix is A ...

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Standard XII

Mathematics

Matrix Definition and Representation

Construct 2 ×...

Question

Construct $2 \times 2$ matrix, $A = [a_{i j}]$ whose elements are given by
$(i i) a_{i j} = \frac{(i)}{j}$

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Solution

Here, $A = {[\begin{matrix} a_{11} & a_{12} a_{21} & a_{22} \end{matrix}]}_{2 \times 2}$ , where $a_{i j} = \frac{i}{j} .$
$∴ a_{11} = \frac{1}{1} = 1, a_{12} = \frac{1}{2}, a_{21} = \frac{2}{1} = 2 a n d a_{22} = \frac{2}{2} = 1$
Hence, the required matrix is $A = {[\begin{matrix} 2 & \frac{1}{2} 2 & 1 \end{matrix}]}_{2 \times 2}$

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Construct 2×2 matrix,A=[aij] whose elements are given by (ii)aij=(i)j

Here, A=[a11a12a21a22]2×2, where aij=ij. ∴a11=11=1,a12=12,a21=21=2 and a22=22=1 Hence, the required matrix is A=[21221]2×2

Construct $2 \times 2$ matrix, $A = [a_{i j}]$ whose elements are given by
$(i i) a_{i j} = \frac{(i)}{j}$