Question

1-Construa a matriz A (aij) 2x3 tal que aij = 5 .i – j .
4- Construir a seguinte matriz : A (aij)2x2,tal que a11= 1 a12= 5 a21= -3 a22= -5

Answer 1

Explicação passo-a-passo:

1)

$\sf A=\Big(\begin{array}{ccc} \sf a_{11} & \sf a_{12} & \sf a_{13} \\ \sf a_{21} & \sf a_{22} & \sf a_{23} \end{array}\Big)$

$\sf a_{ij}=5i-j$

• $\sf a_{11}=5\cdot1-1~\Rightarrow~a_{11}=5-1~\Rightarrow~a_{11}=4$

• $\sf a_{12}=5\cdot1-2~\Rightarrow~a_{12}=5-2~\Rightarrow~a_{12}=3$

• $\sf a_{13}=5\cdot1-3~\Rightarrow~a_{13}=5-3~\Rightarrow~a_{13}=2$

• $\sf a_{21}=5\cdot2-1~\Rightarrow~a_{21}=10-1~\Rightarrow~a_{21}=9$

• $\sf a_{22}=5\cdot2-2~\Rightarrow~a_{22}=10-2~\Rightarrow~a_{22}=8$

• $\sf a_{23}=5\cdot2-3~\Rightarrow~a_{23}=10-3~\Rightarrow~a_{23}=7$

$\sf \red{A=\Big(\begin{array}{ccc} \sf 4 & \sf 3 & \sf 2 \\ \sf 9 & \sf 8 & \sf 7 \end{array}\Big)}$

4)

$\sf A=\Big(\begin{array}{cc} \sf a_{11} & \sf a_{12} \\ \sf a_{21} & \sf a_{22} \end{array}\Big)$

$\sf \red{A=\Big(\begin{array}{cc} \sf 1 & \sf 5 \\ \sf -3 & \sf -5 \end{array}\Big)}$