Question

Considere a matriz a=(aij)50x50 tal que:

Answer 1

Soma diagonal principal:

log 2²+log 2^4+log 2^6 +log2^8 +.....+ log 2^100

= log 2  *(2+4+6+9+.....+100)

2+4+6+9+.....+100  é uma PA

a1=2

an=100

n=50

Sn=(a1+an)*n/2

Sn=(2+100)*50/2=2550

soma diagonal principal = log 2 * 2550 =767,626

Soma diagonal secundária

log 6^(100-1) +log 6^(98-2)+ +log 6^(96-4) +....+log 6^(2-50)

log 6^(99) +log 6^(96)+ +log 6^(92) +....+log 6^(-48)

=(99+96+92+....-48)  * log 6

(99+96+92+....-48) é uma PA

a1=99

an=-48

r=-2

n=50

Sn=(99-48)*50/2=1275

Soma diagonal secundária =1275 * log 6 = 992,143