Question

If matrix A = $[aij{]}_{3\times 2},$ and $aij=(3i-2j{)}^2$, then find the matrix A.

Answer 1

$A={\left[a_{ij}\right]}_{3\times 2}\left(\text{given}\right)$

Matrix $A$ has $3$ rows and $2$ columns.

Therefore,

$A=\left|\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\\ a_{31}& a_{32}\end{array}\right|$

Also,

$a_{ij}={(3i-2j)}^2\left(\text{Given}\right)$

Therefore,

$a_{11}={(3\times 1-2\times 1)}^2=1$

$a_{12}={(3\times 1-2\times 2)}^2=1$

$a_{21}={(3\times 2-2\times 1)}^2=16$

$a_{22}={(3\times 2-2\times 2)}^2=4$

$a_{31}={(3\times 3-2\times 1)}^2=49$

$a_{32}={(3\times 3-2\times 2)}^2=25$

Therefore,

$A=\left|\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\\ a_{31}& a_{32}\end{array}\right|=\left|\begin{array}{cc}1& 1\\ 16& 4\\ 49& 25\end{array}\right|$