Question

construa as matrizes do tipo 4x4 em que:
A=(aij)= 2I²+3J

Answer 1

Explicação passo-a-passo:

Matriz genérica :

(a11 a12 a13 a14)

(a21 a22 a23 a24)

(a31 a32 a33 a34)

(a41 a42 a43 a44)

A=(aij)= 2I²+3J

a11=2.(1)²+3.(1)=2.(1)+3=2+3=5

a12=2.(1)²+3.(2)=2.(1)+6=2+6=8

a13=2.(1)²+3.(3)=2.(1)+9=2+9=11

a14=2.(1)²+3.(4)=2.(1)+12=2+12=14

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a21=2.(2)²+3.(1)=2.(4)+3=8+3=11

a22=2.(2)²+3.(2)=2.(4)+6=8+6=14

a23=2.(2)²+3.(3)=2.(4)+9=8+9=17

a24=2.(2)²+3.(4)=2.(4)+12=8+12=20

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a31=2.(3)²+3.(1)=2.(9)+3=18+3=21

a32=2.(3)²+3.(2)=2.(9)+6=18+6=24

a33=2.(3)²+3.(3)=2.(9)+9=18+9=27

a34=2.(3)²+3.(4)=2.(9)+12=18+12=30

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a41=2.(4)²+3.(1)=2.(16)+3=32+3=35

a42=2.(4)²+4.(2)=2.(16)+8=32+8=40

a43=2.(4)²+3.(3)=2.(8)+9=16+9=25

a44=2.(4)²+3.(4)=2.(16)+12=32+12=44

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Substituindo teremos :

(5 8 11 14)

(11 14 17 20)

(21 24 27 30)

(35 40 25 44)