Question

am nevoie de ajutor

Answer 1

ca matricea sa fie inversabila, det A diferit de 0

deci calculam

detA= -1+0+0-6-0-0

detA=-7 diferit de 0 deci matricea este inversabila

acum A× A la -1=A la -1 ×A=I³

notam A la -1 cu a b c

d e f

g h i

deci

1 0 3 a b c 1 0 0

-1 1 0 × d e f = 0 1 0

2 0 -1 g h i 0 0 1

si facem calculele; inmultim deci cele 2 matrici

a+3g b+3h c+3i 1 0 0

-a+d -b+ e -c+f = 0 1 0

2a-g 2b-h 2c-i 0 0 1

asadar avem:

a+3g=1

b+3h=0

c+3i=0

d-a=0=> a=d

e-b=1

f-c=0=> c=f

2a-g=0=>2a=g

2b-h=0=>2b=h

2c-i=1

a+3g=1

a+3×2×a=1

7a=1

a=1/7 => g= 2/7 =>d=1/7

b+3h=0

b+3×2×b=0

7b=0

b=0=> h=0

e-b=1

e-0=1

e=1

{c+3i=0/×2

{2c-i=1

{2c+6i=0

{2c-i=1

---------(-)

7i=-1

i=-1/7

2c-i=1

2c+1/7=1

2c=6/7

c=3/7=> f=3/7

deci A la -1 = 1/7 0 3/7

1/7 1 3/7

2/7 0 -1/7