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

    (i) a_{ij} = \frac{(i + j)^2}{2}

Answers (1)

A = [a_{ij} ]

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

Each element of this matrix is calculated as follows

       a_1_1 = \frac{(1+1)^{2}}{2} =\frac{2^{2}}{2}=\frac{4}{2}=2                                       a_2_2 = \frac{(2+2)^{2}}{2} =\frac{4^{2}}{2}=\frac{16}{2}=8

      a_1_2 = \frac{(1+2)^{2}}{2} =\frac{3^{2}}{2}=\frac{9}{2}=4.5                                    a_2_1 = \frac{(2+1)^{2}}{2} =\frac{3^{2}}{2}=\frac{9}{2}=4.5

 

             Matrix A is given by

 A = \begin{bmatrix} 2&4.5 \\4.5 & 8 \end{bmatrix}

 

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