Question

1) :A= (aij)3x3 onde aij=i-2j, contrua a matriz A.
2) : A=(aij)2x2 e b (bij)2x2 onde aij = i+j e bij =2i-j construa a matriz a e b
3) : construa A= (aij) 3x3 sabendo que :
se i=j , aij = 1 + i+ j
se =\ j , aij = i-j

Answer 1

Matriz genérica.

 $A= \left[\begin{array}{ccc}a11&a12&a13\\a21&a22&a23 \\ a31&a32&a33\end{array}\right]$


1)
aij=1-2j
a11=1-2.1=-1
a12=1-2.2=-3
a13=1-2.3=-5
a21=1-2.1=-1
a22=1-2.2=-3
a23=1-2.3=-5
a31=1-2.1=-1
a32=1-2.2=-3
a33=1.-2.3=-5

$A= \left[\begin{array}{ccc}-1&-3&-5\\-1&-3&-5\\-1&-3&-5\end{array}\right]$



2)aij=i+j
a11=1+1=2
a12=1+2=3
a21=2+1=3
a22=2+2=4

$A= \left[\begin{array}{cc}2&3\\3&4\end{array}\right]$

bij=2i-j
a11=2.1-1=1
a12=2.1-2=0
a21=2.2-1=3
a22=2.2-2=2

$B= \left[\begin{array}{cc}1&0\\3&2\end{array}\right]$



3)se o i=j o aij=1+i+j
a11=1+1+1=3
a22=1+2+2=5
a33=1+3+3=7

se i ≠ j o aij=i-j
a12=1-2=-1
a13=1-3=-2
a21=2-1=1
a23=2-3=-1
a31=3-1=2
a32=3-2=1


$A= \left[\begin{array}{ccc}3&-1&-2\\1&5&-1\\2&1&7\end{array}\right]$