Question

3)Construa a matriz A=(ajj)3×2 tal que ajj=1,sei=j
i2,sei#j

Answer 1

$A=(a_{ij})_{3\times2}\qquad{a}_{ij}=\begin{Bmatrix}1,\quad\text{se }i=j\\i^2,\quad\text{se }i\ne{j}\end{matrix}\\\\\\A_{3\times2}=\left[\begin{array}{aaa}a_{11}&a_{12}\\a_{21}&a_{22}\\a_{31}&a_{32}\end{array}\right]\\\\\\a_{11}=1,\quad\text{pois }1=1\\a_{12}=1^2,\quad\text{pois }1\ne2\qquad\longrightarrow{a}_{12}=1\\a_{21}=2^2\longrightarrow{a}_{21}=4\\a_{22}=1\\a_{31}=3^2\longrightarrow{a}_{31}=9\\a_{32}=3^2\longrightarrow{a}_{32}=9\\\\\\A=\left[\begin{array}{aaa}a_{11}&a_{12}\\a_{21}&a_{22}\\a_{31}&a_{32}\end{array}\right]\longrightarrow\boxed{A=\left[\begin{array}{aaa}1&1\\4&1\\9&9\end{array}\right]}$