a) Let A = 0 -0 2 1 0 0 1 2 0 b) Determine whether b = Find null(A).. is a solution of the homogeneous system given above. 1 2 c) Let T(X)= AX. Determine whether c = -2 0 d) (i) Determine whether the columns of the matrix A, given in problem 8, are linearly independent. (ii) If not, eliminate a column so that the remaining columns are linearly independent. is in the range (T)..

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6). Determine the solution for the following augmented matrix for a 3x3 linear system of equations. y r3 6. (x, y, z) = ( ) -9 18 Lo 7 | 14. O ON

1. A system of linear equations can be described in a matrix equation Ax = b with 2 -1 1] A = |1 1 2,x = |y| and b = |b2 [-1 5 4] a. Determine if the columns of the matrix A span R³. Give your arguments. b. If the system is homogeneous, describe the trivial solution of the system (if any) in parametric vector form. Also, give a geometric description of the solution set. Give the clear argument. c. If the system is nonhomogeneous and consistent, describe b in parametric vector form. Give the clear argument. d. If b, = 5, b2 = -3, bz = 0, is the system consistent? Give valid argument. Find the solution set of the system. Compare the solution set with the trivial solution of the homogeneous system in b.