4.    Construct a 2 × 2 matrix, A = [a_{ij} ], whose elements are given by:

        (iii) a_{ij} = \frac{(i+2j)^2}{2}

Answers (1)

  (iii)

 a_{ij} = \frac{(i+2j)^2}{2}

      a_1_1 = \frac{(1+(2\times 1))^{2}}{2}= \frac{(1+2)^{2}}{2}=\frac{3^{2}}{2}=\frac{9}{2}                               a_2_2 = \frac{(2+(2\times 2))^{2}}{2}= \frac{(2+4)^{2}}{2}=\frac{6^{2}}{2}=\frac{36}{2}=18

      a_2_1 = \frac{(2+(2\times 1))^{2}}{2}= \frac{(2+2)^{2}}{2}=\frac{4^{2}}{2}=\frac{16}{2}=8                  a_1_2 = \frac{(1+(2\times 2))^{2}}{2}= \frac{(1+4)^{2}}{2}=\frac{5^{2}}{2}=\frac{25}{2}                                       

 

Hence, the matrix is given by

  A = \begin{bmatrix} \frac{9}{2}& \frac{25}{2} \\ 8 & 18 \end{bmatrix}

 

 

 

 

 

 

 

 

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