and write the answer in vector form in terms of the paramete

and write the answer in vector form in terms of the parameters t and s. Find conditions on a and b such that the system {x + ay = 1 x - by = 2 is inconsistent. True or False ? Any two 4-vectors span R^3 The columns of a 3 Times 6 matrix span R^3.

Solution

For a system of equation : px+qy=r and mx+ny=s to be inconsistent, following condition should be met:

p/q=m/n    ____(1)

Comparing the given equation with above system,

p= 1, q= a, m= 1 and n= -b.

Hence, 1/a = 1/(-b)

Therefore, a = -b