Problem 1:

Consider the (3 *J)- matrix over IR that is displayed in cells AM-E13 of the Excel file, View it as the augmented matrix of a linear system over IR in the variables x, *, *s, x4. ( a) Find the parametric form and parametric vector form of a general solution of this system. ( b) Using your solution in part (a), write the general solution of the associated homo- geneous system in parametric vector form,Consider the ( 4x4)-matrix over IR that is displayed in cells AT7 - D20 of the Excel file Call the first three columns of this matrix U, U2, s, and call the last column V. ( A) If possible, express the vector i as a linear combination (over IR) of ahitkills. ( b ) Are the vectors Uh,the, Us Linearly independent? State your reason clearly.\fConsider the (4x4)-matrix A over IR that is displayed in cells A24-D27 of the Excel file. (a) Find the reduced row echelon form of A.( p) Are the columns of A Linearly independent? State your reason clearly. (c) Does the matrix equation Ax= b have a solution for each beIRk2 State your reason clearly