Problem 1. (8 points) Consider the following matria: 1 3 3 2 A = 3 7 1 2 0 1 4 3 (1) Does the system A5? = 6 have a nontrivial solution? Justify your answer. (Don't do more than you need to in order to answer this questions). (2) Describe the solution set to Af = 6 in vector parametric form. (3) Let ail-'3 be columns of A, in order from left to right. Are (id's linearly independent? Justify. If your answer is negative give a linear dependence relation between a} 's (4) Which columns of A correspond the free variables in 5? Describe these columns of A as a linear combination of those columns that correspond to the basic variables in E. (Hint. Use your solution (5) Consider the Span{dl,a2,a3,a4}. Which one of thea -'s you can remove form the spanning set {531,012, a3_: (14} without changing the span space. Justify your answer. (6) Suppose b E R3 and you know that b - a1 + a2 + (1'3. Without calculating b, write the solution to the A5 b explicitly in the vector parametric form