Question

Seja a matriz A = (aij)3x4 tal que

aij =i - j , então a11 + a34 é igual a:

ajudemmm

Answer 1

Devemos criar a matriz genérica de ordem 3x4.

$\large\sf \left[\begin{array}{cccc}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\a_{31}&a_{32}&a_{33}&a_{34}\end{array}\right]$

Agora devemos achar os devidos valores de a11 , a21 , a31 , a12 , a 22 , a32, a13 , a23 , a33 , a14 , a24 , a34. Vamos lá.

$\large\begin{array}{lr} \sf a11 = i-j = 1-1= \underline{\boxed{\red{\sf 0}}}\\\\\sf a21 = i-j = 2-1 = \underline{\boxed{\red{\sf 1}}}\\\\\sf a31 = i-j = 3-1 = \underline{\boxed{\red{\sf 2}}}\\\\ \sf a12 = i-j = 1-2 = \underline{\boxed{\red{\sf -1}}}\\\\ \sf \sf a22 = i-j = 2-2 = \underline{\boxed{\red{\sf 0}}}\\\\\sf \sf a32= i-j = 3-2 = \underline{\boxed{\red{\sf 1}}}\\\\\sf \sf a13 = i-j = 1-3 = \underline{\boxed{\red{\sf -2}}}\\\\\\\end{array}$

$\large\begin{array}{lr} \sf a23 = i-j = 2-3 =\underline{\boxed{\red{\sf -1}}}\\\\\sf a33 = i-j = 3-3 =\underline{\boxed{\red{\sf 0}}}\\\\\sf a14 = i-j = 1-4 =\underline{\boxed{\red{\sf -3}}}\\\\\sf a24 = i-j = 2-4 =\underline{\boxed{\red{\sf -2}}}\\\\\sf a34 = i-j = 3-4 =\underline{\boxed{\red{\sf -1}}}\end{array}$

Com isso podemos trocar os valores da matriz genérica 3x4 por:

$\large\sf \left[\begin{array}{cccc}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\a_{31}&a_{32}&a_{33}&a_{34}\end{array}\right] \Longleftrightarrow \large\sf \left[\begin{array}{cccc}0&-1&-2&-3\\1&0&-1&-2\\2&1&0&-1\end{array}\right]$

Então, agora basta somarmos o termo a11 pelo termo a34. Ficando assim:

$\large\begin{array}{lr}\sf a11 + a34 =\\\\\sf 0 +(-1)=\\\\= \underline{\boxed{\red{\sf -1}}}\end{array}$

Espero ter ajudado.

Bons estudos.

• Att. FireClassis.