Question

Descompuneti vectorul v=3i-2j dupa vectorii a=5i+3j si b=-2i+3j
URGENT!!! ​

Answer 1

Răspuns:

v=ma+nb   m,n∈R

ma=5mi+3mj

nb=-2ni+3nj

3i-2j=5mi+3mj-2ni+3j

3i-2j=(5mi-2ni)+(3mj+3j)

3i-2j=(5m-2n)i+3(m+n)j=.>

Sistem

{5m-2n=3

{3(m+n)= -2<=>3m+3n= -2

Inmultesti prima ecuatie 3 ,pe a 2-a cu- 5 si le adui

15m-6n-15m-15n=9+10

-21n=19

n= -19/21

inlocuiesti pe n= -19/21 in prima ecuatie si aflii pe m

5m-2*19/21=3

5m=3+38/21

5m=(63+38)/21

5m=101/21

m=101/21:5=101/105

v=101/105i-19/21j

Explicație pas cu pas: