1. When you begin LINALG use Disk Operations and Load the Matrix file MAT07.MAT and the Vector file VEC07.VEC. Use the procedure on p. 147 of the text and the ROW OPERATIONS program to find a basis for the subspace of R^5 spanned by the 5 vectors x1, ..., x5 that are stored in VEC07.VEC. For your convenience those vectors have been stored as the columns in a matrix called M1 (SOMETIMES guinea pigs are helped out by those who appreciate their help!). Check your answer by using the REDUCED ECHELON FORM program on M1.
2. The vectors v1, v2, v3, v4 in VEC07.VEC are a basis for R^4, and the vectors u1, u2 are linearly independent. Use the procedure on p. 148 and the REDUCED ECHELON FORM program to extend u1, u2 to a basis by adjoining some of v1, ..., v4. This time, for your convenience, the vectors u1, u2, v1, ..., v4 have been made the columns in the matrix M2.
3. The file MAT07.MAT also contains a matrix A. Find the dimension of the space of solutions of the homogeneous system AX = 0. Indicate clearly which programs were used to obtain your answer.
