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) = \frac-2*1+3*12 = \frac-2+32 = \frac2 = \frac12`

`C_(12) = \frac-2*1+3*22 = \frac-2+62 = \frac42 = 2`

`C_(21) = \frac2 = \frac-4+32 = \frac-12 = \frac12`

`C_(22) = \frac2 = \frac-4+62 = \frac2 = 1`

`C_(31) = \frac2 = \frac-6+32 = \frac2 = \frac32`

`C_(32) = \frac-2*3+3*22 = \frac-6+62 = \frac02 = 0`

Then the matrix is

`C = \begin{bmatrix}\frac12 & 2 \\\\ \frac12 & 1 \\\\ \frac32 & 0\end{bmatrix} = \frac12 \begin{bmatrix}1&4\\1&2\\3&0\end{bmatrix}`