Question

Sendo a matriz A=(aij)2x3 tal que aij = i + 3j, pede-se:
a) A matriz A.
b) A matriz oposta de A.
c) A matriz transposta de A.​

Answer 1

Explicação passo-a-passo:

$A=\left[\begin{array}{ccc}a_{11} &a_{12} &a_{13} \\a_{21} &a_{22} &a_{23} \\\end{array}\right]$

$aij=i+3j\\\\a_{11} =1+3.1=1+3=4\\a_{12}= 1+3.2=1+6=7\\a_{13} =1+3.3=1+9=10\\a_{21} =2+3.1=2+3=5\\a_{22} =2+3.2=2+6=8\\a_{21} =2+3.3=2+9=11$

a)

$A=\left[\begin{array}{ccc}4 &7 &10\\5 &8&11 \\\end{array}\right]$

b)

$-A=-\left[\begin{array}{ccc}4 &7 &10\\5 &8&11 \\\end{array}\right]\\\\-A=\left[\begin{array}{ccc}-4 &-7 &-10\\-5 &-8&-11 \\\end{array}\right]$

c)

$A^{t} =\left[\begin{array}{ccc}4&5\\7&8\\10&11\end{array}\right]$