Let S be the of all column matrices b1b2b3 such that b1,b2,b3∈ℝ, and the system of equations (in real variables) Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution of each b1b2b3∈S?

We find D=0 & since no pair of planes are parallel, so there are infinite number of solution s  Let αP1+λP2=P3⇒  P1+7P2=13P3⇒b1+7b2=13b3A) D≠0⇒ unique solution for any b1,b2,b3B) D=0, but P1+7P2≠13P3C) D=0  Also b2=−2b1,b3=−b1 but b1+7b2=13b3  hence two simultaneous equations in  can be considered as two different planes hence line of intersection has only common solutions other solutions are not common hence C is Not CorrectD) D≠0