Question

1 – Represente explicitamente as Matrizes Abaixo :

a) (aij) de ordem 2 x 2, em que ai j= i2 + 2j.

b) (bij) de ordem 2 x 2, em que bi j= i2 - 2j.

c) (cij) de ordem 2 x 2, em que ci j= 2i + j2.

d) (dij) de ordem 2 x 2, em que di j= 2i - j2

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Answer 1

a)

$\mathsf{a_{11}=1^2+2.1=1+2=3}\\\mathsf{a_{12}=1^2+2.2=1+4=5}\\\mathsf{a_{21}=2^2+2.1=4+2=6}\\\mathsf{a_{22}=2^2+2.2=4+4=8}$

$\huge \: A=\begin{bmatrix}3&5\\6&8\end{bmatrix}$

b)

$\mathsf{b_{11}=1^2-2.1=1-2=-1}\\\mathsf{b_{12}=1^2-2.2=1-4=-3}\\\mathsf{b_{21}=2^2-2.1=4-2=2}\\\mathsf{b_{22}=2^2-2.2=4-4=0}$

$\huge~B=\begin{bmatrix}-1&-3\\2&0\end{bmatrix}$

c)

$\mathsf{c_{11}=2.1+1^2=2+1=3}\\\mathsf{c_{12}=2.1+2^2=2+4=6}\\\mathsf{c_{21}=2.2+1^2=4+1=5}\\\mathsf{c_{22}=2.2+2^2=4+4=8}$

$\huge~C=\begin{bmatrix}3&6\\5&8\end{bmatrix}$

d)

$\mathsf{d_{11}=2.1-1^2=2-1=1}\\\mathsf{d_{12}=2.1-2^2=2-4=-2}\\\mathsf{d_{21}=2.2-1^2=4-1=3}\\\mathsf{d_{22}=2.2-2^2=4-4=0}$

$\huge~D=\begin{bmatrix}1&-2\\3&0\end{bmatrix}$