Question

Construct a 3×3 matrix whose general element is given by aij=2i-j

Answer 1

Step-by-step explanation:

i think this solution will help you, in this I have just placed the value of the places of the terms in the matrix in the equation....

Answer 2

Answer:

$\text { The required matrix } A=\left[\begin{array}{lll}1 & 0 & 1 \\3 & 2 & 1 \\5 & 4 & 3\end{array}\right]\end{aligned}$

Explanation:

$a_{i j}=|i-2 j|$

The general $3 \times 3$matrices is

$\begin{aligned}&A=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23} \\a_{31} & a_{32} & a_{33}\end{array}\right] \\&a_{11}=|2(1)-(1)|=|2-1|=1 \\&a_{12}=|2(1)-1(2)|=|2-2|=0 \\&a_{13}=|2(1)-1(3)|=|2-3|=|-1|=1\end{aligned}$

$\begin{aligned}&a_{21}=|2(2)-1|=|4-1|=3 \\&a_{22}=|2(2)-(2)|=|4-2|=2 \\&a_{23}=|2(2)-(3)|=|4-3|=1 \\&a_{31}=|2(3)-(1)|=|6-1|=5 \\&a_{32}=|2(3)-(2)|=|6-2|=4 \\&a_{33}=|2(3) -(3)|=|6-3|=3 \\&\text { The required matrix } A=\left[\begin{array}{lll}1 & 0 & 1 \\3 & 2 & 1 \\5 & 4 & 3\end{array}\right]\end{aligned}$