Problem 1: Consider the following system 2x1 + X2 + X3+ 3 x42 X2 + X3 + X4 = 2 2 x3 2 x4 0 a) Rewrite the system in matrix form: A = b b) Using Gauss-Jordan eliminations, please reduce the system Ai- b down into its reduced row-echelon equivalent Rx = 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 (ii) Using arrows and text, label the pivot columns and the "free variable" columns within R A U Now, we are ready to solve for the "complete solution" x to our Ax = (0 + ) problem, where is actually a hidden vector that's buried within our original Ax- b equation. By explicitly including 0 on the right- hand side, we can now express the complete solution as a combination of 2 separate solution types xn- homogeneous (nullspace) solutions when A--0 i - Xn + Xp . where = The particular solution when Axp- b c) What are the nullspace solutions Xn and the particular solution Xp for our problem? Hint: Your answer must include the most-trivial nullspace solution for all Ax problems !! 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 IRm. 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 of A g) Look at your complete solution -X+ Xp again. Does our original equation Ax- b have an uniue solution, no solutions, or an infinite number of solutions? Explain your answer in terms of what you just wrote down for