Question

represente explicitamente cada uma das matizes.

Answer 1

Olá


i = linhas
j = colunas



A)

Lei de formação da matriz:

$\mathsf{A = (a_{ij})_{3\times2}~tal ~que~a_{ij}~=~i+2j}$


$\mathsf{A= \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\\a_{31}&a_{32}\end{array}\right] }\\\\\\\mathsf{a_{11}~=~1+2\cdot 1 ~=~\boxed{3}}\\\\\\\mathsf{a_{12}~=~ 1+2\cdot 2~=~\boxed{5}}\\\\\\\mathsf{a_{21}~=~2+2\cdot 1 ~=~\boxed{4}}\\\\\\\mathsf{a_{22}~=~2+2\cdot 2~=~\boxed{6} }\\\\\\\mathsf{a_{31}~=~ 3+2\cdot 1~=~\boxed{5}}\\\\\\\mathsf{a_{32}~=~3+2\cdot 2~=~\boxed{7 }}$


$\boxed{\mathsf{A= \left[\begin{array}{ccc}3&5\\4&6\\5&7\end{array}\right] }}$




B)

Lei de formação da matriz:

$\displaystyle \mathsf{A = (a_{ij})_{2\times3}~tal ~que~a_{ij}~=~ \left \{ {{1,~se~ i = j} \atop {i+j, ~se~i\neq j}} \right. }$


$\mathsf{A= \left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\\end{array}\right] }\\\\\\\mathsf{a_{11}~\Longrightarrow~1=1\Longrightarrow a_{11}~=~\boxed{1}}\\\\\\\mathsf{a_{12}~\Longrightarrow~1\neq2 \Longrightarrow a_{12}~=1+2~=~~\boxed{3}}\\\\\\\mathsf{a_{13}~\Longrightarrow~1\neq3 \Longrightarrow a_{13}~=1+3~=~~\boxed{4}}\\\\\\\mathsf{a_{21}~\Longrightarrow~2\neq1\Longrightarrow a_{21}~=2+1~=~~\boxed{3}}\\\\\\\mathsf{a_{22}~\Longrightarrow~2=2\Longrightarrow a_{22}~=~\boxed{1}}$

$\mathsf{a_{23}~\Longrightarrow~2\neq3\Longrightarrow a_{23}~=2+3~=~~\boxed{5}}\\\\\\\\\\\boxed{\mathsf{A= \left[\begin{array}{ccc}1&3&4\\3&1&5\\\end{array}\right] }}$





C)

Lei de formação da matriz:

$\mathsf{A = (a_{ij})_{2\times2}~tal ~que~a_{ij}~=~(-1)^{i+j}}$


$\mathsf{A= \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\\\end{array}\right] }\\\\\\\mathsf{a_{11}~= ~(-1)^{1+1}~=~(-1)^2~=~\boxed{1}}\\\\\\\mathsf{a_{12}~= ~(-1)^{1+2}~=~(-1)^3~=~\boxed{-1}}\\\\\\\mathsf{a_{21}~= ~(-1)^{2+1}~=~(-1)^3~=~\boxed{-1}}\\\\\\\mathsf{a_{22}~= ~(-1)^{2+2}~=~(-1)^4~=~\boxed{1}}\\\\\\\\\boxed{\mathsf{A= \left[\begin{array}{ccc}1&-1\\-1&1\\\end{array}\right] }}$