Question

Dane są dwa wektory : a=[3,-1] oraz b=[5,3] . Znajdź takie wektory x , aby :
a) 2*x+3*a=b
b) 1/3*x+b=2a
c) x=3*a-1/2b
d) 1/2*b=-1/2a-2*x
e) 3*(x-a)=2*(x+b)

Answer 1

A)
2x=b-3a  /:2
x=1/2b-3/2a
x=1/2*[3,-1]-3/2*[5,3]=[3/2,-1/2]-[15/2,9/2]=[-6,-5]
b)
1/3x+b=2a /*3
x=6a-3b
x=6*[3,-1]-3*[5,3]=[18,-6]-[15,9]=[3,-15]
c)
x=3a-1/2b=3*[3,-1]-1/2*[5,3]=[9,-3]-[5/2,3/2]=[13/2, -9/2]
d)
2x=-1/2a-1/2b   /:2
x=-1/4a-1/4b
x=-1/4*[3,-1]-1/4*[5,3]=[-3/4,1/4]-[5/4,3/4]=[-2,-1/2]
e)
3x-3a=2x+2b
3x-2x=3a+2b
x=3a+2b
x=3*[3,-1]+2*[5,3]=[9,-3]+[10,6]=[19,3]