The vector (m 2-n) a+(2n 2+n) b is based on e 1, e2, and the decomposition formula is 2e 1+3e2, a=e 1+e2, b=e 1-e2,

A and b are two nonparallel vectors. Find the values of m and n.

Solution:

(m？ -n)a+(2n？ +n)b

=(m？ -n)(e 1+e2)+(2n？ +n)(e 1-e2)

=(m？ -n+2n？ +n)e 1+(m？ -n-2n？ -n)e2

=(m？ +2n？ )e 1+(m？ -2n？ -2n)e2

=2e 1+3e2

According to the basic theorem of plane vector, we can get

m？ +2n？ =2

m？ -2n？ -2n=3

Subtract two expressions: 4n? +2n+ 1=0

Because delta = 2? -4×4 & lt； 0

So there is no solution.