Let A be a 3times3 matrix with two pivot positions. Use this information to answer parts​ (a) and​ (b) below. a. Does the equation Upper A Bold x equals Bold 0 have a nontrivial​ solution? A. No. Since A has 2​ pivots, there are no free variables. With no free​ variables, Upper A Bold x equals Bold 0 has only the trivial solution. B. Yes. Since A has 2​ pivots, there is one free variable. The solution set of Upper A Bold x equals Bold 0 does not contain the trivial solution if there is at least one free variable. C. No. Since A has 2​ pivots, there is one free variable. Since there is at least one free​ variable, Upper A Bold x equals Bold 0 has only the trivial solution. D. Yes. Since A has 2​ pivots, there is one free variable. So Upper A Bold x equals Bold 0 has a nontrivial solution. b. Does the equation Upper A Bold x equals Bold b have at least one solution for every possible b​? A. Yes. A has a free variable. So the free variable can equal any value such that there is at least one solution for every possible b. B. No. A has one free variable. To have at least one solution for every possible b​, A cannot have any free variable. C. Yes. Since A has 2​ pivots, there are no free variables. So there is at least one solution for every possible b. D. No. A has one free​ variable, so there will be no solution to the system for any possible b.