Lab Assignment #3, Linear Algebra - part I 1. Use the Mathematica command, LinearSolve, to solve the the system of equations Axb, where A = -1 2 -2 -1 1 1 1 -1 2 1 -2 -2 2 1 -1 1 1 3 -2 1 -3 -3 3 2 -2 -2 2 4 0 0 2 -1 1 2 -2 5 1 -1 0 -3 3 and b= x+z 2x+y+z 3x + 2y + 2z 5 0 6 -4 1 Use the MatrixForm command to display your arrays/vectors, but don't use matri- ces/vectors in calculations that have been defined using the MatrixForm function (see the last page). 2 5 -3 2 2. Use the Transpose and Append commands, to construct the augmented system, [Ab]. (Note: the Append command applied to A and b appends b as a row of A, so you will have to append b to the transpose of A and then take the transpose of the appended result.) Use the RowReduce command to get the row-reduced echelon form of the augmented system. What is the rank of A? What is incomplete with the results of Problem 1? 3. Solve the system of equations using Cramer's Rule. Use matrix multiplication to verify that you have obtained the solution. See the D