Question

Construct a matrix of order 3×2 whose elements are given by Cij=|−2i+3j|/2

Answer 1

$C_{ij}$ is the entry of $C$ in row $i$ and column $j$. $C$ has 3 rows and 2 columns, so

$C_{11} = \dfrac{|-2\times1+3\times1|}2 = \dfrac{|-2+3|}2 = \dfrac{|-1|}2 = \dfrac12$

$C_{12} = \dfrac{|-2\times1+3\times2|}2 = \dfrac{|-2+6|}2 = \dfrac{|4|}2 = 2$

$C_{21} = \dfrac{|-2\times2+3\times1|}2 = \dfrac{|-4+3|}2 = \dfrac{|-1|}2 = \dfrac12$

$C_{22} = \dfrac{|-2\times2+3\times2|}2 = \dfrac{|-4+6|}2 = \dfrac{|2|}2 = 1$

$C_{31} = \dfrac{|-2\times3+3\times1|}2 = \dfrac{|-6+3|}2 = \dfrac{|-3|}2 = \dfrac32$

$C_{32} = \dfrac{|-2\times3+3\times2|}2 = \dfrac{|-6+6|}2 = \dfrac{|0|}2 = 0$

Then the matrix is

$C = \begin{bmatrix}\dfrac12 & 2 \\\\ \dfrac12 & 1 \\\\ \dfrac32 & 0\end{bmatrix} = \dfrac12 \begin{bmatrix}1&4\\1&2\\3&0\end{bmatrix}$