Question

{a, b, c} i. p. {-2, 7, -3}
-a+b+3c=21

{a,b,c} i. p. {1,5,-4}
-6a-3b+c=20​

Answer 1

Răspuns:

Explicație pas cu pas:

{a, b, c} i. p. {-2, 7, -3}

-a+b+3c=21  <=>

-2a = 7b = -3c  => a = -7b/2

c = -7b/3  =>

7b/2 + ²⁾b - ²⁾7b = ²⁾21 =>

7b+2b-14b = 42  => -5b = 42 =>

b = -42/5 = -8,4

a = (-7/2)·(-42/5) = 294/10 = 29,4

c = (-7/3)·(-42/5) = 294/15 = 19,6

a = 29,4  ; b = -8,4 ; c = 19,6

-29,4-8,4+3·19,6 = 58,8-37,8 = 21

{a,b,c} i. p. {1,5,-4}

-6a-3b+c=20​ <=>

a = 5b = -4c =>

a = 5b ; c = -5b/4

⁴⁾-6·5b -⁴⁾3b -5b/4 = ⁴⁾20 =>

-120b-12b-5b = 80 =>

-137b = 80  => b = -80/137

a = -400/137

c = 100/137

-6·(-400/137) -3·(-80/137) +100/137 =

= (2400+240+100)/137 = 2740/137 = 20