Question

若a=-e1+3e2,b=4e1=4e2,c=-3e1=12e2.则向量a写为λ1b+λ2c的形式

Answer 1

a=-e1+3e2, b=4e1+4e2,c=-3e1+12e2

a = λ1b+λ2c

-e1+3e2 = λ1(4e1+4e2)+λ2(-3e1+12e2)

= (4λ1-3λ2)e1+(4λ1+12λ2)e2

=>

-1= 4λ1-3λ2 (1) and

3= 4λ1+12λ2 (2)

(2)-(1)

15λ2=4

λ2=4/15

λ1=-1/20

ie

a = (-1/20)b+(5/15)c