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Questions  >>  CBSE XII  >>  Math  >>  Matrices
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Q)

Construct a 2 x 2 matrix, $A=[a_{ij}],$whose elements are given by: $\;a_{ij}=\frac{(i+2j)^2}{2}$

Note: This is a 3 part question, split as 3 separate questions here

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A)
Toolbox:
  • In general $a_{2\times 2}$ matrix is given by $\begin{bmatrix}a_{11} & a_{12}\\a_{21} & a_{22}\end{bmatrix}$
  • Elements are given by $a_{ij}=\frac{(1+2j)^2}{2}, $where (i,j) can be (1,1,) (1,2), (2,1) or (2,2)
Given,, $a_{ij}=\frac{(1+2j)^2}{2}, \Rightarrow$
$a_{11}=\frac{(1+2(1))^2}{2}=\frac{(1+2)^2}{2}=\frac{3^2}{2}=\frac{9}{2}.$
$a_{12}=\frac{(1+2(2))^2}{2}=\frac{(1+4)^2}{2}=\frac{5^2}{2}=\frac{25}{2}.$
$a_{21}=\frac{(1+2(1))^2}{2}=\frac{(2+2)^2}{2}=\frac{4^2}{2}=\frac{16}{2}=8.$
$a_{21}=\frac{(1+2(2))^2}{2}=\frac{(2+4)^2}{2}=\frac{6^2}{2}=\frac{36}{2}=18.$
Hence the required matrix is given by $A=\begin{bmatrix}\frac{9}{2} & \frac{25}{2}\\8 & 18\end{bmatrix}$
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