For each of the following sets, show that the set is or is not a subspace of the appropriate R". {[x1 x2] | x1 + x2 = 1} {[x1 x2 x3] | x1 + x2 0} {[x1 x2 x3] | x1 - 2x2 = x3, x1 + x2 = 0} Row reduce the following matrices to obtain a row equivalent matrix in row echelon form. Show your steps. Show that each of the following sets is linearly dependent by writing a non-trivial linear combination of the vectors that equals the zero vector. {[1 1 1], [2 2 2]} {[3 -2 4], [1 2 -1], [-6 4 -8]} {[2 1 2], [5 4 5], [1 1 1]} Each of the following matrices is an augmented matrix of a system of linear equations. Determine the values of a, b, c, d for which the systems are consistent. In cases where the system is consistent, determine whether the system has a unique solution.
