Problem 2: Consider the following system 2x1 + X2 xi +x23 x1 + x2 x1X2- a) Rewrite the above in matrix form: Ai-b b) using Gauss-Jordan eliminations, please reduce the system Ax = b down into its reduced row-echelon equivalent Ri - d. When expressed in augmented matrix form, this means: Gauss-Jordan eliminations Show work by indicating (i) All the row operations required in going from: A U R (ii) Circle all pivots when you are going from: (iii) Using arrows and text, label the pivot columns and the "free variable" columns within R AU Now, we are ready to solve for the "complete solution" i to Ai - (O b) ,where Xn- homogeneous (nullspace) solutions when Axn0 i-X + Xp . where = The particular solution when Ax-b c) What are the nullspace solutions n and the particular solution X for our problem? d) The nullspace N(A) is a subspace of R. What is the dimension number"n"? e) The column space C(A) is a subspace of Rm. What is the dimension number"m"? f What is the rank of our matrix A ? Also, does the column space C(A) span a line, a 2D plane, a 3D volume, or something larger? Explain your answer in the context of either the rank or the span of the column vectors ofA g) Write down the complete solution as a single, non-zero vector h) Finally, ask yourself: Does our original equation Ax= b have an unaue solution, no solutions, or an infinite number of solutions? Explain your answers in the context of the solution your wrote in part (g)