Question

If a matrix has $18$ elements, what are the possible orders it can have? What, if the has $5$ elements?

Answer 1

Since matrix has $18$ elements,
$\text{No. of rows}\times \text{No. of columns}=18$
$1\times 18=1818\times 1=18$
$2\times 9=189\times 2=18$
$3\times 6=186\times 3=18$
Hence, possible orders are
$1\times 18,2\times 9,3\times 6,18\times 1,9\times 2,6\times 3$

If matrix has $5$ elements.
$\text{No. of rows}\times \text{No. of columns}=5$
$1\times 5=5$ or $5\times 1=5$
Hence, possible orders are $1\times 5$ and $5\times 1$.