Question

If A = [a_ij] is a 2 × 2 matrix such that a_ij = i + 2j, write A.

Answer 1

Here

`a_ij = i + 2j, 1≤ i≤2 and 1≤ j≤2`

\[ \therefore a_{11} = 1 + 2\left( 1 \right) = 3, a_{12} = 1 + 2\left( 2 \right) = 1 + 4 = 5\] 

`⇒ a_21 = 2 + 2( 1)==4 and a_22 = 2 + 2( 2 ) = 2 + 4 = 6`

\[ \therefore A = \begin{bmatrix}a_{11} & a_{12} \\ a_{21} & a_{22}\end{bmatrix} = \begin{bmatrix}3 & 5 \\ 4 & 6\end{bmatrix}\]